If it can be done on or in the water, Michigan probably offers at least a little of it, somewhere in the state. Fishing, sailing, and motorboating are popular on both the Great Lakes and inland lakes. The Great Lakes are a bit cool for some tastes, even in the summer, but are still very popular beach destinations, along with swimming in the warmer lakes inland. Canoeing is also popular on the rivers snaking through protected forests. Some people do surf, mostly the often-substantial waves coming across Lake Michigan, but it won't impress the dudes back home at Hermosa Beach or Waimea.
In winter, replace water with snow and ice. Hardcore anglers keep fishing through the ice. Although serious alpine skiers might find the idea of skiing in glacier-smoothed Michigan laughable, there are many downhill ski areas, with the most popular resorts in the still-textured Charlevoix/Grand Traverse region of the state. Some great cross-country skiing can be found in both peninsulas, and any incline with a population of kids nearby becomes a sledding hill.
The city of Detroit hosts four major professional sporting teams: the Tigers baseball (http://detroit.tigers.mlb.com), the Lions American football (http://www.detroitlions.com), the Red Wings hockey (http://www.detroitredwings.com), and the Pistons basketball (http://www.nba.com/pistons/). The Lions, Red Wings and Tigers all play in stadiums in downtown Detroit; the Pistons play in Auburn Hills approximately 25 miles northwest of Detroit. Detroit also hosts the North American International Auto Show (http://www4.naias.com) each January. Big-city casino gambling with four major casinos supplementing the several Native American casinos in more remote areas of the state is Detroit's latest addition. Detroit serves as the cultural and entertainment hub of the metropolitan region, with major concert venues, the Detroit Symphony Orchestra (http://www.detroitsymphony.com), the Detroit Institute of Art (http://www.dia.org), and an active theatre scene.
In Lansing, you can visit the State Capitol Building, which was renovated in 1992. Many other state government and historical buildings are located in Lansing and East Lansing.
There are many small towns of interest in Michigan. Frankenmuth, a town in Mid-Michigan, is a replica German town. Very famous is the Zendher's and Bavarian Inn, two restaurants known for their fried chicken.
If crossing from the Lower to Upper Peninsula, or vice-versa, visit Mackinaw City, St. Ignace, and Mackinac Island. Fort Michilimackinac and an old lumber mill are located on the latter, and these are both open to the public. In order to get to the Island, you must take a ferry. Three different services are available.