With one exception, Food Services at MLB parks are provided/managed by four companies: Aramark, Centerplate, Delaware North Companies Sportservice, and Levy Restaurants. The exception is the Florida Marlins; Dolphin Stadium is serviced by Boston Culinary.
Warning: there can be more than one provider because Concessions and Premium (suites, club seats, etc) options are generally not the same - no prime rib or lobster in the cheap seats. Levy is pretty well focused on Premium. Here's my first attempt at a breakdown. Corrections - not to mention advice on adding tables - welcome.
Arizona - Levy Atlanta- Aramark Baltimore- Aramark Boston- Aramark Chi. Cubs- Levy Chi. White Sox- DN Sportservice Cincinnati- DN Sportservice Cleveland- DN Sportservice Colorado- Aramark Detroit- DN Sportservice Florida- Boston Culinary Houston- Aramark Kansas City- Aramark / Centerplate LA Angels- Aramark LA Dodgers- Levy Milwaukee- DN Sportservice Minnesota- Aramark / Centerplate NY Mets- Aramark NY Yankees- Centerplate Oakland- Aramark / ? Philadelphia- Aramark Pittsburgh- Aramark / Levy San Diego- DN Sportservice San Francisco- Centerplate Seattle- Centerplate St. Louis-DN Sportservice Tampa Bay- Centerplate Texas- DN Sportservice Toronto- Levy Washington- Aramark