Yes, Chesterfield! I wasn't going to recommend because it's out of the city a bit and OP wanted closer to the zoo area, but this is where we stay pretty much every time (Drury, of course). It is right on I-64 and pp was right, it's about 25 minutes. Easy drive to anywhere, just avoid rush hour times.
This one is a Drury Plaza which is a step up from a regular one. I just checked and tried the "stlfun" promotional code and it worked - showing a rate of $79.99 a ntie (put in 3/20), which is fantastic. You would NOT be disappointed here. All the extras you get, I don't know how they can be that cheap. Between the free breakfast and free food in the evenings (not full on meals, but you could get away with eating dinner there - chicken strips, hot dogs, that kind of stuff), you could really save some money. And each adult gets free alcoholic drinks every evening as well.
Also, you have Trader Joe's just down the road and are across the street from Chesterfield Mall which is one of the best malls in St. Louis area. Also, this one has a Cheesecake Factory. Yum. Oh, let me wipe away that drool. We don't actually eat there often, but will stop and pick up cheesecake to bring back to the hotel. If you keep going west on I-64 they have a super, super long strip mall with lots of shops and restaurants (including Chick-Fil-A, which is always a novelty for us!).
Chesterfield also down the road from the Butterfly House, but to me it's a little expensive unless you have a coupon.
Good luck!!!