I would say that there are several areas nearby where I could have parked my 36' + toad for a couple hours. You might have to loop around looking but there's industrial areas and side streets. Also, if I recall correctly, there's a park right at the beginning of the river walk that might fit the bill...as long as you don't get there on a weekend or holiday. You'd have to park covering several spaces length wise. (Going by memory on that, but typically, when I go somewhere to tourist, I check on that sort of thing). In fact, try to get there on a week day in any event.
I stayed at a campground north of town and drove my car down, but felt there were several side streets I could have parked on. I was there in April this year.