Id suggest paying the money and parking in a lot close to the statium. Dont leave valuables in the car. Unfortunately, St. Louis downtown is only active right before and directly after a cards (any sports) game. Then everyone clears out. If you are headed to Iowa, after the game head west and stay anywhere west of I270. but, dont stay north of 70 on 270. Downtown st charles has alot of things happening by the river front. areas to stay include Creve Couer, Ballwin, Chesterfield, St Charles, St Peters, Ofallon, Wentzville.
It is quite a shame that we have to warn people where to stay, but there are regularly stories on the evening news where a family is staying at a hotel, or visiting an attraction, and all their luggage/ valuables gets stolen along with their car. The St. Louis politicians cant even figure out to police the touristy areas.