Yes, there is plenty of trailer parking in the lots just upriver of the dome. Do take care that you will have an outlet when you enter a lot that is full or nearly so. I drove our trailer into a long dead-end path one afternoon last year, and I am not sure exactly how I managed to back out and get turned around without losing a bumper.
Edit: My New Orleans is showing again. In the case of the dome in St. Louis, upriver is actually north.
Edit2: Using Google Maps, there are five such lots, all bordering N 6th St.
This link is right in the middle of them.