Places to eat:
Metro Diner - On 11th between Delaware & Harvard - good old fashioned diner.
Embers Steak House - 81st and Harvard - the best steak house in Tulsa (a little expensive, but WORTH it)
Shogun - Japanese hibachi grilling. Exceptional food cooked right in front of you. My favorite is the Samurai.
In The Raw - If you're into sushi, this is the place to get it. There are two locations - one in Brookside and one just south of 61st and Sheridan.(I'd suggest the 61st & Sheridan location).

Things to do:
If the Drillers are in town, take in a baseball game. If not, you can try the Philbrook Museum of Art, Gilcrease Museum, the Oklahoma Aquarium (in Jenks), Bell's Amusement Park. It really depends on what you enjoy doing.

How to get around:
You'd better have a car. Preferably one with a terrific suspension. We've got a lot of construction (Highway 169 between I-44 and I-244, I-244 in west Tulsa, Highway 75 near 71st Street). I'd say the bus sucks and there really isn't much other travel option except a cab, which I wouldn't suggest either.

Tried to post a comment for him but I'm not that sophisticated (or patient)...so I'll just tell you that my Tulsa friend, who loves the fine dining, raves about Bodean Seafood Restaurant. It doesn't look like much, but he says its the best. (http://www.bestoftulsa.com/tulsamenus/bodean_seafood.shtml/)

I would also recommend the Philbrook if he has any time on his hands. http://www.philbrook.org/DesktopDefault.aspx