Long story short, you could get most anything you could in San Francisco in the frontier -- just in lower quantities, higher cost and considerable delay. It would take me longer to find menus from some of the saloons during that time but during my researches on Arizona history I've certainly come to see that saloons had a large selection from which to draw.
That said, the individual saloons were responsible for assembling the goods available to them into dishes - so what actually made it to the table might be different than what was available in the town.
It seems most saloons offered some sort of victual, usually in the form of breads and dry goods.
Fresh Bread and Pies at the Bakery and Coffee Saloon --- Arizona Miner (Fort Whipple, Arizona) 05 Oct 1864, Wed Page 4
Above this advert is an advert for French pies and cakes. I assume this means French in style, not imported.
More Fresh Bread, Pies, Cakes plus Oysters, Sardines, 'etc.' In addition to fresh lager beer, wines, cigars, etc. -- The Weekly Arizona Miner (Prescott, Arizona) 29 Jul 1871, Sat Page 4
Provisions of all kinds available in larger cities were somewhat available to the frontier -- saloons could draw on these to serve. Flour, Bacon, Lard, Pickles, Crackers, Butter, Tea, Coffee, Sugar, Dried Fruit (and fresh fruit from local trees), Canned Fruit, Meat, Fish, Vegetables and other 'groceries & provisions' (such as honey and whatever local farmers had on hand) --- Arizona Miner (Fort Whipple, Arizona) 13 Jul 1867, Sat Page 3
An abundance of fruit trees in Tucson --- The Weekly Arizonian (Tubac, Arizona) 24 Mar 1859, Thu Page 3
While railroads accounted for most of the ease of trade; they began in Arizona in 1866, a lot of these sources are from 1865+. Pickings were much slimmer in 1855 - but where there was a town there were stagecoaches and mule teams trading food. Arizona is on the way to and from San Francisco and so benefitted greatly from the gold rush traders and the routes they carved.
1879 - No shortage of competition - this is in Maricopa county With 78 Saloons and 23 Restaurants, competition could be stiff.
Also, it should be noted that the availability of food and drink would change over these decades. While San Francisco had ballooned to a population of 25,000 over the course of a year in 1849, Arizona was virtually unoccupied except for forts and Native Americans at the time; the oldest incorporated city in Arizona, Tucson, only dates to 1877. Thus you could expect to see a lifestyle on par with the big East Coast cities in San Francisco by the 1870s, but Arizona would still be rough and tumble until the 1880s and 1890s.
California was the first place to start seeing the wealth from gold and silver mining. Prices rapidly fluctuated in the market in 1850, going as high as 2000% markup on canned fruit and bags of flour and dropping just as much. But restaurants quickly formed, as many of the miners were inexperienced cooks who had previously relied on their wives at home to do the cooking. Menus from 1849 show hot chocolate, oxtail soup, steak, stews, lamb tenderloin, and all sorts of wines and beer.
Out in the countryside, things got more difficult. The usual food of the time was the Three B's: biscuits, bacon, and beans washed down with plenty of coffee (or "coffee" made from roasted whatever as a substitute). They were non-perishable for the most part, so you could easily transport them long distances. Out west away from the big coastal cities like San Francisco in this time period, you could expect food like this just about anywhere, along with hunted game when available.
Things started changing in the 1870s and 1880s thanks to the Transcontinental Railroad, which was finished in 1869. As it became cheaper to transport goods across the country and refrigerator cars began seeing widespread use in the 1880s, it started becoming easier for these frontier towns to receive food from miles away. You started seeing saloons in the desert with crystal chandeliers offering imported oysters on ice and hiring chefs who could whip up at least imitations of the fancy French-influenced cuisine of the big cities.