In what city, in what country? This is important because the modern affinity for enjoying different kinds of exotic cuisine in one city is well, modern. Before the 20th century started local cuisine was local, traditional local dishes with almost all ingredients sourced locally.
There were not many restaurants in America in the higher end category 200 years go, this started taking off more in the mid 19th century. New York already had established it's current reputation for steak and chop houses though, and oyster houses, and New Orleans for creole, the local variant on classic French cooking with menus tailored to local seafood and game. Boston, as now, was a seafood town with clams crabs and saltwater fish popular. This was generally tavern and inn food, local country cooking served in a very informal atmosphere by a home trained cook. The very first French chefs who opened restaurants in the Us started to emigrate right around the turn of the century, with American restaurants in the fine dining style starting to pick up in the 1820's-1840's.
Most European capitals at that time had enough traffic passing through for diplomacy, trade, and internal governance to support restaurant traffic. Until the late 18th century this also would have been limited mainly to taverns and inns though. The modern concept of fine dining is really an unintended consequence of the French Revolution. So many aristocratic manors were closed with the families either dead or gone that an entire class of highly trained chefs suddenly found themselves out of work and on the street all at once. With tavern eating fairly fashionable they started applying the advanced skills they had once used to entertain the aristocracy to the open marketplace. At the same time the power of old cooking guilds was broken by the new system allowing chefs a tremendous amount of freedom to experiment and offer variety. This meant anyone with money could walk up to a building, be given a seat, be offered a meal for a fixed price and have a tremendous variety of meal options prepared by a world class chef for the first time. This is where the modern concept of fashionable and artistic cuisine in restaurants really emerged.
As far as the menu goes, 200 years ago is right after the French Revolution, we are actually very close to the 200 year anniversary of Napoleon's first exile. So the restaurants at this time are at their very earliest state of development in France, and elsewhere still more low brow. Also, like today different restaurants did things differently.
Food options are dominated by the food sourcing of that era. Everything is local, food that was transported any distance would have likely been barreled and salted, or pickled. Also, everything is seasonal, no fresh fruit and vegetables year round.
One likely form for a "menu" would be something like the modern prix fixe menus, where the restaurant charges a flat fee to serve a multi course meal. The dishes would be the best the chef could put together using seasonally available ingredients that were available that day. Alternately (and more popular on the high end of the scale) the idea of having choice was a huge draw for early restaurant customers, and some restaurants specialized in this, with menus that to the modern sensibility were incredibly busy and crowded, with dozens of options in every single category (entrees, soups, desserts, etc.). These restaurants would have had large dining areas, music, and proper service loosely based on (formerly) aristocratic standards.
As for the food itself, or specific recipes? Wild game would have been a more common sight, and the cuts of meat would have been more variegated, with items like sweetbreads, tongue, head/face/jowl being prized over the more modern lean cuts from the flanks and ribs. The cooking was mainly the mode of what we now consider "classic" French cuisine, the kinds of things you find in Julia Child's cookbook, which is full of recipes that go back hundreds of years.
There are some interesting histories on restaurants, part of the emerging and fascinating scholarship going into food in general in the last 30-40 years. A History of Cooks and Cooking by Michael Symons covers this early era, as does the Oxford Companion to Food.
If you want a free online translation of a very early bit of writing on the subject here is a link to a translation of the 1825 The Physiology of Taste, by Brillat-Savarin. It is full of choice little nuggets on specific dishes and the manner in which they were prepared and served, and probably answers your question specifically:
So I searched for you but the oldest menu I could find was American House a Boston restaurant, from January 1, 1851. (Not quite 200 years ago, I know I'm off by a few decades.) As you can see, they served fish chowder, boiled salmon with shrimp sauce, turkey and oysters, stewed pigeons, omelet and jelly, various roasts, as well as puddings and pastries.
I help the NYPL (and you can too!) digitize and transcribe these menus. The reason we have this menu, and others like it from this time, is because of a remarkable but little known woman named Miss Frank E. Buttolph (1850-1924), whose mission in life was to collect menus. In 1899, she offered to donate her existing collection to the Library and to keep collecting on the Library's behalf. The director at the time accepted her offer and for the next quarter century Miss Buttolph continued to add to the collection. There was very little method behind her collection; she would simply write to every restaurant she could think of asking of their menus. When letters failed, she often marched into a restaurant and pleaded her case in person. She also placed advertisements in trade publications like The Caterer and The Hotel Gazette, but just as often, published news of her collection prompted outright contributions of specimens from around the world. Because of her, the NYPL was given over 25,000 menus. Three times between 1904 and 1909, The New York Times wrote about her and the collection, noting once that >"she frankly avers that she does not care two pins for the food lists on her menus, but their historic interest means everything."
150 years close enough? This is in Paris 1870. More details/sources below
Café Voisin, G. Braquenas
HORS D'ŒUVRE
Beurre - Radis - Tête d'âne farcie - Sardines
POTAGES
Purée de haricots rouges aux croûtons
Consommé d'éléphant
ENTREES
Goujons frits - Le chameau rôti à l'Anglaise
Le civet de Kangourou
Côtes d'ours rôties sauce poivrade
ROTS
Cuissot de loup, sauce chevreuil
Le chat flanqué de rats
Salade de cresson
La terrine d'antilope aux truffes
Cèpes à la bordelaise
Petits pois au beurre
ENTREMETS
Gâteau de riz aux confitures
DESSERT
Fromage de gruyère
VINS
PREMIER SERVICE DEUXIEME SERVICE
Xérès Mouton Rotschild 1846
Latour Blanche 1861 Romanée Conti 1858
Ch. Palmer 1864 Bellenger frappé
Grand porto 1827
Café et liqueurs
There are plenty of other menus available from this time and beofre, but some of the sources are iffy at best or not stated at all. That being said, what they list is very much what they would have had, so there is little doubt of its reality. ex: dinner menu for Marie Antoinette on July 24th, 1788 is easy enough to check in one of her biographies. Her life was well enough documented.
Some restaurants have claims to have existed for far longer than 200 years, but little to no documentation can prove it.
Here is a menu from 1751: http://www.cuisinealafrancaise.com/img/uploaded/HDC/18%C3%A8me%20si%C3%A8cle/menu_1751_vignette.jpg
That being said, restaurants were not common for high end affairs, they ate in stately homes and were private affairs. The meals were very long with tons of dishes. Fois Gras, oysters, soups, all sorts of fish and shell fish. Roasts were complete, like a pig on a spit that roasted for 24 hours or more. pigeon, pheasant, and all the game you can think of.
In France at least, cafes started being common in the early 18th century, but these were places of discussion and meetings, not what we are looking for. The first restaurant as we know them was most likely in 1765 were one could "be served at individual tables, at any time, soups, roast chicken, fruits, cheese" Until then, you could eat at fixed times in inns and pubs and these were fixed menus (table d'hote).
http://www.cuisinealafrancaise.com/fr/articles/17-histoire-de-la-cuisine
I can get more sources later when I get home.
hope this helps.
Like /u/digifox6, I'm a few decades off, but Stephane Mallarme was a French poet known for hosting salons attended by the intellectual class at the time (He lived in the latter half of the 19th century). Mallarme wrote a women's fashion magazine called La derniere mode which was full of peculiar articles, including menus for various occasions. In Mallarme on Fashion, a critical reading of the text, the commentators note that "he appears to have been both a gourmet and a gourmand.", and is described as both a ferocious eater and in his earlier life as too poor to have eaten at expensive restaurants.
Most of the text is available here, and if you CTRL+F "Menu", I think you'll be able to easily find all of them. There are two "Menu for a Grand Dinner", which might be of particular interest.
That said, this is from 1870's France, so limited in scope and not really the timeline you're looking for.
I know that you are looking for restaurants 200 years ago, but if you are interested, there is an article on food and performance in the Song and Yuan dynasty (960-1368). It describes that restaurants specialized in food from distant regions (instead of local) were created in this period to accomodate travelers for example, and the various dishes that were served, among other things.
Stephen H. West, ''Playing With Food: Performance, Food, and The Aesthetics of Artificiality in The Sung and Yuan''. Harvard Journal of Asiatic Studies, Vol. 57, No. 1 (Jun., 1997), pp. 67-106
edit: here is a link. http://www.academia.edu/1535293/Playing_with_Food_Performance_Food_and_the_Aesthetics_of_Artificiality_in_the_Song_and_Yuan
as one of the oldest and most complex of the world's 'mother cuisines', there is a long history of enjoying exotic foods and elaborate preparations in chinese cooking. [written records of culinary culture date back to the 8th century ce, in which preparations of expensive and difficult game such as bear and camel can be found.] (http://en.wikipedia.org/wiki/History_of_Chinese_cuisine#Tang_Dynasty) the tradition of enjoying such fare has been preserved through millenia, even to the current day, where modern restaurants recreate the [imperial feasts of the qing dynasty] (http://en.wikipedia.org/wiki/Manchu_Han_Imperial_Feast). a blend of a taste for the exotic and unusual, as well as beliefs about the health effects of foodstuffs rooted in traditional medicine, has resulted in the sometimes notorious stereotype of chinese cuisine including every ingredient known to man.
since we are discussing 'high-end' restaurants, it is helpful to keep in mind that in imperial times, exclusivity was not solely defined by price. for example, restaurants in beijing were classified by official decree according to their culinary ability and clientele, and the highest-end restaurants served royalty and nobility exclusively. therefore, if we are interested in the specifics of the menus, we look at the foods of the emperor's court, as those tend to be well documented and had significant overlap with what was served in the restaurants of the day.
in general, historical chinese cuisine reflected the diverse range of ingredients including domesticated animals (pig, sheep, chicken, duck, dog), wild game (quail, deer, bear, tiger) and whatever the fishermen managed to catch/scavenge in the water. grains like wheat, millet, sorghum, and oats were (and still are) consumed in the dry north, while rice was the staple of the south. in addition, there are the spices and foods of central asia, south asia, and the near east, brought through trade on the silk road and other routes (cumin, jujube, figs, mangos). for perishable items, a rapid transit horse courier system was set up specifically to transport things like lychee fruit and blocks of ice for the imperial court. these ingredients were then combined to dizzying effect and produced an elaborate menu. examples include:
most of the sauces and condiments associated with chinese food that we're now familiar with (soy sauce, rice vinegar, sesame oil, fermented tofu) were in production by the 10th century. there would have been dishes recognizable as 'chinese food' by the song dynasty. tea, beer, wine, and spirits would have been consumed as well.
EDIT: for clarification, 200 years ago puts us at 1814, in the second half of the qing dynasty.
Hope that you were in france and not britain