Are you interested in things like MN State Parks? I guess I'm wondering if you are looking for swimming, playgrounds, hiking, camping, or what more specifically.
We love Glendalough State Park, just NW of Alexandria in the Battle Lake area. They have a lake that is canoe or rowboat only (no noisy motors) and "heritage fishing" so there is really great panfish fishing if you are into that. There is another lake there with a beach, nice hiking trails, and cart-in sites.
Glacial Lakes State parks has prairie hiking and private backpacker campsites, and there are interesting historical sites out west too (Ft. Ridgely, Upper & Lower Sioux agencies.) But maybe those places are better for older kiddos..
Up north, Itasca, Jay Cooke and some of the Lake superior State parks were favorites of mine as a kid, and they have neat junior naturalist programs.
As far as the Twin Cities, I love Minnehaha Falls mentioned above. There are also some outdoor water/ splash parks (Richfield, St. Anthony, St. Paul). We also like to take our LO to hidden beach of Cedar Lake, kindof a mellow hippie vibe there compared to other city beaches (and a mud pit!) Eloise Butler Wildflower gardens and the nearby bog walk in north Minneapolis are also fun.
Oh, this makes me so excited that summer is almost here!!!