Up North MI is big,, but I will throw out some restaurants worth checking out. Will start from the south and head north..
Big Rapids MI - Schuberg's Bar (rated one of the top ten burgers in MI this year)
Cadillac MI - Hermann's European Cafe (esp the escargot and Jager Schnitzel "Hunter's Style")
Gaylord MI - Gobbler's (save room for pie, or do like my wife and I do and have it first.. The Applejack Turkey sandwich is my favorite)
Indian River MI - Wilson's River Edge Restaurant ( only been there once, was really good, hear they have amazing breakfast)
Millersburg MI - Three Cedar's (used to be the Millersburg Inn and was closed more than it was open, but some new blood bought it and are doing a great job with it..)
St Ignace MI - Clyde's Drive In.. (Also rated one of MI top 10 burgers this year)
Brevort MI - White Tail resort I think it's called. (Little greasy spoon on the east side of Brevort on the north side of Rt 2. Really good food and amazing bread pudding)
Munising MI - Navigator (have only had breakfast there, but also really good food)
Houghton MI - Victoria's Kitchen (only open for breakfast and lunch, I have only eaten breakfast there, but eat there every opportunity I get. Vicky makes really great food!)
As for what else to do besides eat, especially if going to the UP grab these two books, they will keep you busy
199 MI WaterfallsTraveler's Guide to MI lighthouses