Rexberg ain't too bad, but coming from SD, get ready for a culture shock. I went to school just south of there in Pocatello (Go Bengals! haha). Anyway, there are a handful of cool parks in eastern Idaho. As far as I know nobody is kicking bikes out except Blackfoot. That park kinda blows so no big loss.
Idaho Falls has a pretty cool new park they built a couple years ago. St. Anthony is worth the drive. Pocatello's Ross park is so-so. Pokey is better for street sessions though. And there were trails there when I lived there but IDK nowadays. I've ridden Rexberg a handful of times and I always find something interesting to do, and if you can bunnyhop more than 6 inches off the ground I think the mayor actually comes out and shakes your hand, haha!
I make a trip up to ride eastern idaho every summer just cause its nice to ride something different than Salt Lake, this year I might continue onto Montana, I've heard good things.