Lansing is the capital of Michigan. They have a nice capitol building.
There's a lake in the area where you can paddle in these canoes reminiscent of French fur traders.
In the suburb of Okemos you can visit a collection of original buildings and walk the paths through the woods around them. Also near Lansing/Haslett you can take a horse-drawn cart to pick apples, and check out their woods as well.
In summer, you can take a carnival ride in the parking lot of the grocery store, in summer and fall you can see rare black squirrels hoarding for winter, and in winter you can see a LOT of the white stuff. They do an excellent job of plowing, so road conditions are not usually an issue.
And if rock climbing is your thing, you can find plenty of space for that at Grand Ledge, just west of Lansing.