We go to STL several times a year. Never do we stay downtown. IMHO there just isn't enough to do there to justify staying. We were just there Sunday evening for the American Idol concert and I didn't always feel safe. We made a beeline for our destinations - too many people just kind of mulling around. There are definitely some unsafe areas, especially the further north of downtown you get. If you do go to City Museum, be sure to park in their lot! We made the mistake of parking on the street and our van was broken into in broad daylight - very common place in that area. Not trying to discourage anyone from going, just take safety precautions!
I write for a local website and made a St. Louis page last year:
http://springfieldmoms.org/st-louis-day-trips-and-attractions/
We always, always stay at Drury. For the price, you can't beat it with all the amenities you get. We typically stay at the one in Chesterfield. A little out in the burbs but we don't mind the drive a bit. It's just next door to a big mall, which also has a Cheesecake Factory. Lots of nearby shopping & restaurants. With a coupon code, we usually average about $70-100 a night, just depending on the time of year. Love it there! Always feels like home.
You mentioned the zoo AND Grant's Farm. If you are looking for multiple things to do each day, I am hesitant to recommend the zoo. It's HUGE and easily could spend an entire day there. It is free to get in, but their lot isn't (sometimes you can get street parking but you may have a bit of a walk).....and they have the children's zoo area that has an admission fee. Grant's Farm is free, you do pay for parking. If you want something to get through in a few hours, I think GF is a great option!
We just ate @ Fitz's Sunday and it's always a fun place to go.
On the link I shared above, you will find a link to some coupons, one of which is a buy one get one free for Magic House. This place gets busy pretty quickly! We've had the best luck getting there right when they open or later in the afternoon closer to the time when they close.
Another FAVE that we always have to stop at is Yucandu. Fun art studio and a great place to spend a few hours. We have nothing like it in our hometown so it's a special place for my daughter.