tfjim mentioned "The Hill". This is the Italian section of town that has several outstanding Italian restaurants. Charlie Gitto's is also a good choice on the Hill. No trip to St. Louis is complete unless you go to the Hill.

The "best" restaurant in the city is Tony's. Always well rated and great service. Not sure I'd go there on my nickel -- went once with work and another time with a friend's parents.

Other places my wife and I like include Barcelona (Tappas place in Clayton), Nobu (yes, they have good sushi in St. Louis), House of India (good Indian food on Delmar), Fortell's (Best Pizza I've ever had), Protzels (best corned beef around, hands down -- corner of Wydown and Hanley). A few newer places that are good are Sqwires and Space.

And make sure you go to Ted Drewes for desert afterwards for a concrete! My favorite is the Cardinal Sin.