http://www.dnr.state.mn.us/state_parks/map.html
Looks like Minnesota Valley, Frontenac, Afton, and William O'Brien are all within daytrip distance of Minneapolis by bike. If you ask locally, one of them probably gets slammed on weekends with folks looking to "escape to the country". I know there's a particular Madison area park (Devil's Lake) that's supposed to see very heavy use. So pick a localish park, and plan an overnight. If you're worried about being cold, maybe wait til May. But it's not a giant hairy deal to bike to a state park and stay overnight.