The Very Best St. Louis Restaurants.......
You should try "The Crossing", "Araka". Both are not far from your hotel. If you want something little more casual but fun try Niche or Franco in the Soulard area (20 minutes or so from your hotel). Sauce magazine has reviews about all these restaurants. Let us know what you finally chose and how is it. Welcome and enjoy your visit.
2. An American Place
Larry's Forgione's an American Place
822 Washington Avenue, St. Louis, MO 63101
1831 Sidney Street, St. Louis, MO 63104
Atlas Restaurant & Lunch Room
5513 Pershing Ave, Saint Louis, MO 63112
131 Carondelet Plaza, Clayton, MO 63105
It has been around for generations, so it often gets overlooked in favor of trendier, newer places. But for excellent service, consistently fine cuisine (much of it finished tableside), and a dress-up, special occasion ambiance, the top restaurant in St. Louis has been and remains Tony's, downtown near the ballpark on Broadway. Quiet, ornate, some would say staid, with well-spaced tables, it is the classic St. Louis upper-crust restaurant.
I have two recommendations for a very informal lunch in Clayton not too far from your hotel. Cafe Manhattan has a diner-type decor and some of the best St. Louis-style pizza. (While often dissed on this board, I crave and love that pizza, with ultra-thin crust, provel cheese, and cut into squares rather than wedges.) They also make a good rendition of toasted ravioli and a tasty house salad. On Hanley, a touch south of the Clayton offices and civic center. For a great burger, try The Fatted Calf. Great char-grilled burgers with small scoops of soft cheese atop (I like the cheddar, my mom goes for the blue). Near the heart of Clayton.
Some of the replies overlook that the OP asked about "fine dining." Even if you somehow like the StL style of pizza, it will never properly be characterized as fine dining. In any event, I second Niche, American Place and Atlas. I haven't yet tried Araka, but am anxious to do so. I would probably also add Terrene to the list. I question The Crossing. I more than question Tony's. I think the recommended restaurants should be those that would be highly acclaimed in even the major cities of the U.S. Having a formal atmosphere and a doting staff, as Tony's does, doesn't alone put it on the list. The food is really just above average, but nothing spectacular; if it wasn't for the glitz, there'd be no reason to go out of your way to go there. It has the benefit of tradition, but it were a new restaurant that just opened - given the much higher caliber of restaurant competitiion in StL now than in the day when Tony's earned its acclaim - it would not be regarded as a great restaurant.