The Henry Ford Museum is interesting at any time of year. It's like the Smithsonian American History Museum. Next door Greenfield Village is like an 1800s Colonial Williamsburg or Plimoth Plantation. OK in spring, except in rain. The Henry Ford also sells tickets to the Ford Truck Plant which runs M-F and is classically Detroit and very interesting.
Jan-March is winter. Unpredictable snow and rain. April can be lovely early spring with daffodils and tulips. Or grey and rainy like March.
We actually have a famous tulip festival and it's in early May. So that tells you that MI spring is April-May.
https://www.holland.org/tulip-festival/
The DIA is a nice art museum with some famous pictures and good traveling shows.
There are good live music scenes all the time if you are an aficionado of any Detroit genres.
Detroit is close to Canada if you have a passport and would like to try Chinese food in Windsor (I hear good things but don't have recs).
The University of Michigan in Ann Arbor has interesting events. Some of which only travel to a few US cities. Look at the University Musical Society, School of Music, Theatre, and Dance, and events.umich.edu. This semester, I went to an Armenian shadow puppet show and an Indonesian gamelan concert.
I grew up with a northeast background. The Great Lakes lakeshore reminds me a lot of Maine and that type of summering. If you have done that, Michigan will feel familiar.
What do you like to do on vacation, OP? Especially in cities and in rainy weather?