Minnetonka game and fish, which is in Elk River
is a really nice place to shoot, but the waiting list is about 3 years to get in.
Deltone, which is in St. Cloud (about 30 minutes from Elk River) is an OK place to shoot, but no rapid fire (more than 1 round per 2 seconds seems to be the cutoff), so that may be an issue for you if you want to do anything but precision rifle. No wait to get into that club though, just give them your yearly membership fee, and you're in. They do shut the range down during the summer a couple times for events, so be aware there may be a couple weeks when you cannot shoot there.
Not sure what Princeton's all about, I've shot there once and it seems to be a nice place that allows full auto and all kinds of other fun stuff, but I'll have to defer details to someone that knows them.