L.M.
I grew up in Michigan.
Some of my favorite places to visit as a kid (and still) are:
Hartwick Pines - one of the last remaining stands of old growth pine trees in the state, there's a little logging museum type thing, and for a kid, it's just fantastic to run around.
Sleeping Bear Dunes National Lakeshore - these dunes are the best. Hands down, the best.
(I recommend staying in Traverse City and doing two day trips, one west to Sleeping Bear Dunes, and one East to Hartwick Pines).
Head to Petoskey and look for petoskey stones, if you get them wet you can see the pattern a bit better, but for a kid, a stone like that is a real treasure! - it's a 350 million year old piece of coral!
The Au Sable River is really nice, but more for hiking and canoeing so it's probably better for warm weather.
Binder Park Zoo is also great!
A lot of people like Frankenmuth, I've never been a fan.