The Gateway Arch will be several hours. The actual ride up/down/inside doesn't take long, but there is sometimes quite a wait until your group can go up. But you know ya gotta do it! There's normally an interesting documentary to watch on how it was made and a history museum in it also.
The kids will really dig City Museum,
https://www.citymuseum.org and so will mom and dad. You might take in a ball game, and there are great restaurants downtown and nearby. If you narrow down which part of metro STL you'll be staying in, we can recommend things nearby, in case you don't want to stay downtown.
[Edit: In case the link doesn't make it clear, City Museum isn't a museum per se, but has "archived" portions of cities to climb around on, and through. STL has actual museums such as the MO History Museum of course.)
And I recommend the Zoo in Forest Park, which is actually free due to a public subsidy from a cultural tax. You're welcome! (But the Zoo's nice anyway, and there's a nifty narrow gauge railway inside the kids will also like riding.)
And hey, there's a Weber Restaurant, too.