Probably among the earliest variant of what you are talking about is actually the phenomenon of tourist guidebooks, Baedekker guides and the like. I did a big project on tourism a while back and don't have the sources or information on my fingertips anymore, but the vague outline is that it dates in a really commercial sense to the 18th century with the rise of the "Grand Tour" of Europe, a big circle around the continent that primarily young rich British kids would do so they could sow their wild oats where no one knew their name, and come back all 'cultured' from their time on the continent and whatnot. In order the reap the greatest spiritual, cultural, aesthetic, and pleasurable gains, people wrote travel narratives with reviews (one of the most fun being Tobias Smollet's curmudgeonly 1766 account, satirized by Lawrence Sterne, although everyone was writing one for a while, from Robert Louis Stevenson, to Mary Shelley to Lord Byron). Anyway, these soon morphed into a commercial market for traveler's guides, most famous of which are Baedeker guides, est. 1827. These would include reviews and descriptions of museums, food, sights, hikes, roads, and inns. You could become a critic by contributing to these guides, but it was rarely a full-time occupation; Baedekers prided themselves on soliciting contributions from local professors and experts for each book.

A more point-specific answer I can give is about the rise of food criticism, using Rebecca L Spang, The Invention of the Restaurant: Paris and Modern Gastronomic Culture (Cambridge, Mass.: Harvard University Press, 2000). Spang argues that the restaurant (originally offering restorative broths for those tool ill to feed themselves) evolved into its modern form in revolutionary-era France. In the era of Napoleon III (aprox 1799 onward) "Gastronomy exempted itself from incendiary questions of subsistence, and placed the table squarely in the realm of literary or artistic debate." (150) Food criticism as a genre was inaugurated by Grimod de la Reyniere with his 1803 Almanach des Gourmands featuring reviews and critiques of food and restaurants. Soon, the gourmands and food critics emerged as a self-styled meritocratic and apolitical elite within the cultural domain. (And French food critics have arguably been painting themselves as such ever since! Think of the cultural cache of Julia Child's french cooking, or the success of Chez Panisse in California, predicated on French prestige!)