No matter what you do, make your stop for lunch at
Pappy's!
Probably the best BBQ I've ever put in my mouth.
Pappy's is great but the lines are often long.
Same chef, same amazing quality, shorter lines at
Bogart's.
Tons of great suggestions in this thread. The Botanical Gardens are amazing, and if you're in that neck of the woods, be sure to eat at
O'Connels which is only a few blocks away. Also a short drive from the Gardens is the
Shaved Duck, one of the best meals I've had in years.
I'd also second the Transportation Museum if you have boys, but sadly, no food to recommend near there. Best bet would be to drive elsewhere for food - probably back toward the mid-metro area. Tons of great spots in and around Clayton as well.
If you end up in the Loop, near Washington University, either hit up
Pi or
Blueberry Hill, both on Delmar.