I don't know of any specific kayaking groups, but you should stop by Tyrol SKi and Sports and ask for Robb. He knows everything about paddling around here and runs boat demos at Chester Woods (which I think is the best place to go paddling anyway). I also bought this book, which is a great reference: http://www.amazon.com/Canoeing-The-Driftless-Southeastern-Minnesota/dp/1414042043
Check these out. It should be more than enough to get you started.
Upper Mississippi Refuge Water Trails