The Hyatt downtown next to Rupp is a pretty good one..anywhere downtown close to Rupp Arena would be fairly good because you'll be within walking distance to a whole lot of good restaurants and Lexington has a nice downtown area (relatively speaking compared to other big cities)
I'm pretty sure there's a shuttle service that runs from Hyatt but I'm not positive..even if not it's not all that far from campus, etc.
You can get some other ideas as far as restaurants, but it depends what you like. If you want something on the classier/expensive end then Malone's is pretty nice (and expensive)..it's a steakhouse kinda place.
Tolly Ho is a college-aged kid restaurant on campus that's pretty well known. You might not want to go late at night with a bunch of drunks in there, but during the day would probably be fun.
Joe Bologna's is a pizza restaurant on campus that's good. Two Keys and Tin roof are all kind of campus bars that serve food during the day if you want to get a drink and get a bite or something I would suggest something over in that area so you can eat and explore the campus a little if you have time.
You could always make a stop by Keeneland or go look at some of the horse farms around Lexington..others would probably be able to give you some better ideas on what else to do, but hopefully that helps a little.
