While we were in Missouri visiting family, we took the boys for their first visit to the arch. (Tony doesn't remember having gone before, either, but his mom says he went as a preschooler.)
We were there on July 5, technically a holiday, and LOTS of other people joined us. We waited to get through security (similar to an airport), waited to buy tickets to the top, and then waited for our scheduled trip up (1 1/2 hours after we purchased the tickets).
It was lunchtime and the arch has no restaurant (nor were we going to leave to find lunch and wait through the security line again), but the gift shop sold various bagged snacks. Between those and the soda machines, we were able to have a snack picnic while we waited for our scheduled time.
At the ticket line, they have a sample of the elevator you ride to the top. It's there for you to try out to make sure you're not going to get claustrophobic during the 4 minute ride. Here is Jeremiah trying it out:
Mork from Ork, anyone?
Obviously, the 7 of us could not fit in one elevator car. Tony and Joseph rode in one with strangers, while Grammy and Granddad rode with Joshua, Jeremiah and me. I took cell phone pictures in our car, but can't currently upload them.
Once at the top, you are allowed to stay in the viewing area as long as you'd like. There are platforms by the windows to help kids see out:
Here's a view of the new Busch Stadium. The window was smudged.

This next picture is toward the Illinois side of the Arch, though it still shows Missouri since it is taken straight down.
A couple notes about this one: 1) Notice the arch's shadow on the ground. 2) St. Louis has a big 4th of July celebration, which had ended the night before. They were still in the process of taking down the stage, cleaning up trash, etc. Normally the area below would be much cleaner. 3) The Mississippi River (that ugly brown thing at the top of the picture) was above flood stage. Normally there would be more road below (or above, as you look at the picture) where it ends here. 4) See the riverboats in the top right corner? When I was a kid, there was a riverboat McDonalds there. My kids would have loved that, but it is gone now. : ( I wonder how many thousands of pounds of french fries floated their way down to New Orleans after kids dropped them overboard to watch them float?
One final shot, taken from directly under the arch. If you look really closely, you can see the rows of windows at the top.