Former Michigander here and now reside in Tennessee. May is still cool but it can be quite pleasant depending. The long range winter forecast, if one can put any stock into such things, is calling for a warmer than normal winter, whatever that really means. So if you luck out and MI experiences a mild winter and early spring you may have perfect weather in May with daytime temps in the 70's and lows in the 40's.
Must see things depends on your interests. Lots of nature and excellent state parks to stay in. There's The Henry Ford/Greenfield Village in Dearborn and Ford offers tours of their truck plant.
There's Frankenmuth, Michigan's little Bavaria. Great chicken dinners and a few nice CG's in the area. Mackinac city and Mackinac Island are nice and the Mackinac bridge that connects the 2 peninsulas.
The whole of the west Michigan shoreline has quaint towns, from the Traverse bay wineries to huge sand dunes that have to be seen to be believed, down to Holland that has their Tulip festival and their Dutch heritage.
I would order the MI. travel guide or visit the travel web site for ideas too. MI. has lots of RV parks so finding a place to park shouldn't be a problem no matter where you go in the state.