Ok, I like maps, but I suck at drawing. Hopefully this makes sense.
There is a coffee shop to the north of us with a pull through parking lot. You can pull through there, and drop vehicles off of trailers, then pull out and park the truck and trailer on the street. There should be pretty good street parking on Sunday since there is nothing going on downtown. Anything you can find on 400 W, 400 S, or like SnwMnkys said, on 500 W is fair game. The north side of 400 S along Pioneer park has lots of long parking and it should be wide open Sunday. Probably the same on 400 W along the west side of Pioneer Park.