Covered or uncovered?
On-site parking at MSP is the best, but it can run up to $16/day. Park 'n Fly offers both lot and ramp/covered parking and they are the closest lot to the airport. Although, if you go for the covered parking, unless you can use the senior/AAA discount, it's almost the same price as parking on-site and you don't have to take the shuttle bus.
http://www.parknfly.com/minneapolis/default.htm