Edited to add: I really do apologize <...>
No worries. I'm not from here, and there's a lot I don't like about the place, but I actually consdider the food one of the bright spots of living here, so YMMV.
Not to belabor the point, here are roughly 20 places in/around Ann Arbor that have/have had (don't know when the list was compiled by coworker) bebimbop on the menu. I believe Kosmo and Rich J.C. were the top picks on the original bebimbop tour several years ago. We did Tianchu last week, to mixed reviews. I really enjoyed my bebimbop with beansprouts. Others liked the kimchee version. Standard bebimbop was rated good, but overshadowed by the memory of other places (yet to be visited on the new tour).
Arirang 3135 Oak Valley
Bells Diner 2167 W Stadium Blvd
BeWon Korean Cuisine 3574 Plymouth Road
Biwako Sushi (Ann Arbor) 2276 S Main
Biwako Sushi (Saline) 1355 E Michigan Ave, Saline
Broadway Café 1139 Broadway
Hana Korean Restaurant 1346 E Michigan Ave, Ypsilanti
Kang's Korean Restaurant 1327 S University
Kosmo 407 N North 5th Ave (kerrytown)
Lucky Kitchen (Central Campus) 611 E University
Lucky Kitchen (North Campus) 1753 Plymouth Road
Maru 414 E William
Panda Korean and Chinese Restaurant 3020 Packard Road
Rich J.C. Korean Restaurant 1313 S University Ave
Rod's Diner 812 S. State
Seoul Garden 3125 Boardwalk Dr
SeolStreet3 1771 Plymouth Road Suite 101
Teriyaki Time 314 Detroit St
Tianchu Korean Restaurant 613 E. William
University Café 621 Church St
I'd be very interested in trying Mexican food in Detroit. In my travels around the country I have yet to find a decent Mexican restaurant that far North. This is usually due to the lack of real Mexican spices.
In Ann Arbor, there's Sabor Latino -- which is mostly Mexican on weekdays and not-just-Mexican on weekends. Then you have some Mexican grocery/taqueria combo places like Taco King.
(Be warned: on review sites, people just seem to love saying stuff like "not as good as it used to be," etc. about these (and similar kinds of) places. And there's all the standard authentic! no not authentic! stuff.)
In Detroit you have the whole Mexicantown neighborhood. La Gloria bakery is a definite place to visit for Mexican sweets. The story with Mexicantown is that everybody says avoid the tourist strip places and hunt down the small neighborhood restaurants and grocery/taquerias. Me, I've only been to one of the tourist places, and thought it was OK, so I can't make any real recommendations. I person I trust says try Taqueria Lupita's. (I'll have to give it a try myself now.)
Is there a food that Detroit is known for?
Middle eastern, I'd say.