I was born and raised in Tulsa and lived there for 35 years.
Here are a few of my favorites that I hit everytime I'm in town.
BBQ - Elmer's "It be bad" BBQ.
http://www.elmersbbq.net/
Asian - Viet Huong. Though it is owned by a Vietnamese family and have traditional Vietnamese food, they also have Chinese too. The place looks like a **** hole from the outside, but the food is
awesome. It's been voted #1 in T-Town for many many years. Don't do the buffet, order off the menue. When people ask how good it is, I just tell them to imagine that your grandmother was Asain...I eat there several times throughout the week...
Hamburgers - It's a toss up. Hanks Hamburgers has been around since the 1940's. It's small, always crowded but the burgers are great. Goldies Patio Grill has been voted #1 for quite a few years.
Steaks - Jamil's Steak House... Been there forever, pricey but you better go with an appetite. Unbelievable steaks!
Seafood - Another place that looks like a ******** and isn't in the best part of town (but is was a good part of town when they opened in 1932!!!). Unbelievable food!
http://www.whiteriverfishmarket.com
Chili - Ike's Chili House. Hands down, the best in town, it's all they serve... In business since 1908 (no ****).
Coney-I-Lander - Make sure it is one of the
REAL "Coney-I-Lander's" there are a lot of knockoffs there and none of them hold a candle to the orginal. They are small coneys, but DAMN they're good. In business since 1907. There is one on 11th street, 1 mile north from the fairgrounds.
Breakfast - Cottons - For breakfast, most people seem to like Tally's. Probably because it's close to the fairgrounds. But IMO, Cotton's is much better. When you walk in, it feels like you just stepped back in time to the 50's or 60's. The crowd on the weekends is kind of rough, but we go every night after the Chili Bowl and it is usually empty or just a couple of people, it's open 24/7. It's a "greasy spoon" but a great, cheap breakfast with excellent service. If you go after the races, we'll be seated next to the door, drop by and say hi!
Things to see in Tulsa
The Gilcrease museum is awesome if you like that sort of thing.
http://www.gilcrease.org/
Tulsa has a great zoo that is a "sister zoo" to the San Diego zoo.
http://www.tulsazoo.org/
If you like firearms, the J.M. Davis Arms Museum is very, very cool. It's in Claremore, about 25 miles to the east of Tulsa. Well worth the trip. Every type of firearm that has EVER been made.
http://www.state.ok.us/~jmdavis/
The Tulsa Air & Space Museum is pretty cool too.
http://www.tulsaairandspacemuseum.com/