The Flats is really fuc*ing grimey, the only worthwhile place there anymore is Club Heaven, which is full of sl*ts. The Odeon is right there in the Flats, might be able to catch a show if you want. FunkyBuddha is another good club there, although it's not technically in the flats, it's at the top of the hill right off Euclid. House of Blues is close to the Flats too, might be able to catch something decent there depending on when you go. The Warehouse District is much nicer than the Flats, lots of good bars and clubs. The only place I'd avoid is Mercury Lounge, which is full of hipsters and idiots. 6 Street Under is one of my favorites, it's a jazz club.
For food, check out 83 Degrees, Brasa, Johnny's Bistro, Wilbert's, The Watermark, and Century. All of them are your basic restaurants/bars, except 83 Degrees which serves caribbean food, and Brasa, which is $30 for all the prime cut meat you can eat.