There are plenty of cool places to see in the UP like pictured rocks, tahquamenon falls, Kitch-iti-kipi, and Big Spring. There are also some good sounding state parks up there, but I haven't been to any yet.

In the lower peninsula, check out silver lake and sleeping bear dunes. Both have way more sand than I expected to find in Michigan after moving here from the east coast. Sand dunes aside, both have camping and offer plenty of hiking opportunities. There's also Muskegon state Park and PJ Hoffmaster a little further south. These last two are somewhat close to Grand Rapids, which is worth checking out as is the nearby Michigan Adventure and Meijer Gardens and Sculpture park. If you like art and gardens you can easily spend a full day there and get a decent amount of walking in.