Anybody want to take the questionable step of recommending what would qualify something for the list? To pick on GAF, eg, Arthur Bryant's certainly has history and character, but I don't think it's especially good. Whereas a place like Honey 1 might be especially good, but have little history. Of course, I'll ignore all that and start with some favorites that are basically providing quality traditional foods for the region they're in:
MARKETS/SHOPPING AREAS
Tsukiji - Tokyo
Aw Taw Kaw Market - Bangkok, Thailand
Mercado la Merced - Mexico City, Mexico
Mercado de Abastos - Oaxaca City, Mexico
Calle de los Dulces - Puebla, Mexico
Pike Place Market - Seattle, WA, USA
RESTAURANTS/SHOPS
El Bajio - Mexico City, Mexico
Pasteleria Ideal - Mexico City, Mexico
El Moro - Mexico City, Mexico
Dulceria de Celaya - Mexico City, Mexico
Hacienda Teya - Merida, Mexico
Tlayudas Dona Martha - Oaxaca City, Mexico
Super Tortas Puebla - Puebla, Mexico
Taling Ping - Bangkok, Thailand
Heun Phen - Chiang Mai, Thailand
CT Garden - Kuala Lumpur, Malaysia
Black's BBQ - Lockhart, TX, USA
Smitty's BBQ - Lockhart, TX, USA
Cooper's - Llano, TX, USA
Las Manitas - Austin, TX, USA
Babe's Chicken Dinner House - Dallas, TX, USA
Al's Italian Beef - Chicago, Il, USA
Mario's Italian Ice - Chicago, Il, USA
Bortell's - Ludington, MI, USA
DiFara's - Brooklyn, NY, USA
Grimaldi's - Brooklyn, NY, USA
Patsy's - Brooklyn, NY, USA
Katz's - Manhattan, NY, USA
Yonah Schimmel's - Manhattan, NY, USA
Russ & Daughters - Manhattan, NY, USA
Barney Greengrass - Manhattan, NY, USA
Kossar's - Manhattan, NY, USA