Well, I wouldn't exactly call City Museum a children's museum. Our children's museum is called the
Magic House, and while it is excellent, it probably won't appeal much to kids that age.
City Museum, otoh, just might. It's really a funky art installation with "toys" -- for instance, a giant slide made out of a factory conveyor belt. While it certainly appeals to little kids for the play factor, it also appeals to adults for the art factor (and the play factor, too.) The Friday Night cocktail hour is hugely popular with young adults. If you go, I recommend knee pads; it's easy to tear up your knees climbing through the cast concrete tunnels.
As to other things that might appeal to youngsters that age: I'm guessing that they might like the Brewery tour, though they can't drink the free samples at the end of it.
Upper Limits Climbing Gym downtown (by the Union Station Drury) has half-price climbing for youth on Friday nights, and there is a one-of-a-kind trampoline gym out in Chesterfield if you venture out that way, it's called SkyZone.
http://www.skyzonesports.com/OPENJUMP/tabid/58/Default.aspx
My DS12 *loves* both of these places.
If you want to get outdoors, we also have a lot of impressive caves in this area, and canoeing on the Meramec river.
There are tours at all of the stadiums, but you might have to make yourself part of a group to get into them -- you can certainly call and ask. The Fox Theatre also has a really cool backstage tour, but I don't think it will be available that weekend because
A Chorus Line is in town.
The RibAmerica festival at Soldier's Memorial downtown will have food and music on Memorial Day weekend. It's not a really HUGE event, but attracts a good crowd. The same goes for St. Michael's Greek festival, which has just phenomenal food. Gypsy Caravan is that weekend, too -- the mother of all traveling antique fairs. (So you send the boys to the climbing gym and go 'tiquing; the gym and the Caravan are right next door to one another.)
The tourism website is
www.explorestlouis.com.
PS: The Mississippi River always looks dirty because of the strength of the current. It got the nickname "Big Muddy" for a valid reason. St. Louis hosts the Big Muddy Blues Festival on the riverfront on Labor Day weekend.