Here are some fun things:
Saratoga Lanes (http://www.saratogalanes.com/) an old fashioned bowling alley
I concur about City Museum. You really shouldn't miss it. It's not a museum full of paintings and sculpture, but recycled things made into other things that you can play on! Plus, it's open until midnight on Fridays and Saturdays! Really great. Lots of fun. Here's the web site link again: http://citymuseum.org/site/
The London Tea Room is close by. Is good! http://www.thelondontearoom.com/
The Moohla Theater. Big single screen theater, leather couches, cheap popcorn (by theater standards) Drinks available. http://www.stlouiscinemas.com/moolah/
For barbeque, Pappy's Smokehouse
http://pappyssmokehouse.com/ or read an article on the 5 best barbeque restaurants here:
If your a Scotophile, you might like the Scottish Arms restaurant with a great single malt whisky menu! The foot is great too! http://www.thescottisharms.com/
Go up in the Arch if you have time. The museum below is excellent. But make reservations online to go to the top.
And the City Garden is really neat. I think it's a pretty easy walk from the hotel. http://www.citygardenstl.org/
And don't forget one of the *best* indie bookstores ANYWHERE, not just St. Louis, Left Bank Books:
http://www.left-bank.com/ 321 N. 10th, close to the hotel too!
How did I forget Ted Drewes frozen custard?! Wonderful! Though this is kind of a bad time of year for it :(
oh it's never too cold for ted drewes :)
There are some pretty good restaurants on Laclede's Landing as well....The Old Spaghetti Factory, Morgan Street Brewery, etc. It should be a VERY short walk from the hotel.