Right next door is the Impression 5 science museum. While it is aimed at children I've always found it fascinating and it is hands on. Unlike most science museums with which I am familiar they keep building new exhibits.
If you are into history the Michigan History Museum is just South of the Capital. They have an original copy of our state constitution on display. They also got a copy of every computer the state has purchased. Last time I was there they had a room full of old computers. So if you've never seen a Next cube, an Osborne portable, first Compaq portable or an Apple Lisa they are all on display in working order.
https://www.michigan.gov/mhc/museums/mhm
Lastly if you enjoy art visit the Broad Art Museum on the North end of the Michigan State University campus. The building is striking looking and was featured in one of the Batman movies. It is one of the few buildings in America designed by the late Pulitzer prize winning British architect Zaha Hadid.
Course all that pales to Detroit where you could literally spend ten days if you wanted to visit every museum.