Camping is allowed in the little park in Rush Center. Not much there except for a water pump and some grass. When I stayed there, I asked at the fire station next door to the park and they let me sleep on the floor (they also have a bathroom and shower). They used to open the community center across the street to touring cyclists, but they don't do that any more after a bad experience.
Really, there's not much in Rush Center. I have a hard time believing that anybody would bother you if you set up a tent on pretty much any open piece of ground there. For further ideas, ask at the gas station in the center of town. There are always a few old guys sitting around there talking. Or ask at the bar and grill next to the fire station, which is pretty much the only place to eat in town.