Going on the west side of Lake Michigan is waaay out of your way. Plus that would take you through/around Chicago, not to mention Milwaukee. Lots and lots of traffic. Plus that side of the lake isn't very scenic at all (at least until you get to Michigan's Upper Peninsula).
I would highly suggest taking the west side of Michigan (or the east side of Lake Michigan). Michigan's western shore is beautiful. The state parks can be difficult to get into without a reservation during the summer, but you can't beat the dunes, the many, many fruit & veggie farms, and overall beauty. Plus the northern end includes Sleeping Bear National Lakeshore (named the "Most beautiful place in the U.S. by NBC's Today Show a few years ago). Traverse City is also nice and the state park there is very large.
We haul our 5th wheel from SW Michigan to FL for the winters and based upon your starting point in FL, take I-65 north all the way to Indianapolis. A good route north of Indy is US31 through Kokomo and eventually around South Bend, IN. That road will take you north along the lakeshore (hooking up to I-196). There's a nice state park just south of South Haven, MI (Van Buren SP). We've stayed there many times (nice beach). Try to visit Saugatuck, MI just north of South Haven and just south of Holland, MI (also nice state park). Follow the lakeshore north from there via US31 (I-196 splits at Holland toward Grand Rapids). It's basically interstate type driving all the way to Ludington, MI where you'll end up on a nice 2-lane all the way to Traverse City via US31. In fact, you can take US31 almost all the way to Mackinaw City on US31. It will take you through some very nice small towns (Charlevoix & Petoskey).
If you prefer to get to the Mackinac area faster just take I-69 north from Indianapolis through Lansing, MI. From there you will take US127 which will hook up to I-75 near Grayling, MI. From there it's about 1.5 hours to the bridge.
Enjoy Michigan!!! We do.
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