Upper Peninsula:
Don't miss Pictured Rocks. The best way to see it is from the boat tour, it's a 3 hour trip but totally worth it. Or you could use your own kayaks if you have them.
Also a good spot to check out is Tahquamenanon Falls. The upper falls are larger and more grand than the lower falls. There is also a campground there but I have never stayed at it. It is nothing nearly as spectacular as Niagara, but it is 100% NOT commercialized. There are no shops or go-carts, etc. It's all forest and natural. Close to the Falls is White Fish point with an amazing lighthouse and keepers house (my favorite part), and a maritime museum.
If you head over to the Soo Locks there's a restaurant in Sault St. Marie called antlers.....amazing!
Any trip to Michigan makes a trip to Mackinac Island necessary. No vehicles are allowed but you can take or rent bikes. The area is VERY hilly so if you're not in the best of shape, older, or have small children your best bet is to take a horse drawn wagon ride. We got a package deal that included the ferry trip to/from the island, wagon ride, tour of Fort Mackinac, and visit to the blacksmith shop. The island is known for their fudge. In fact on our last trip, we had fudge for lunch.
We used Brimley State Park as our home base for all of these places. We were 1-2 hours from all of the sights we wanted to see. The best part of this park is that you can get sites that back up to Lake Superior. There is a tree line but you can take a path right to the beach.
Lower Peninsula:
Really you can't go wrong with anything on Lake Michigan. Lake Huron is also nice but not as spectacular as Lake Michigan.
Sleeping Bear Dunes is fantastic. It is close to Traverse City, which is very touristy. This area is known for cherries and has a festival every year. You can find cherry everything, salsa, jams, etc.
We go to Silver Lake Sand Dunes in Mears every year. We have a dune buggie we drive or you can rent buggies, quads, etc. We've done this for 16 years, PM me if you want more info.
Ludington is the most sought after state park in Michigan and basically impossible to get into. We did go and it was very nice, but a day trip would be fine as the sites themselves were terrible, (all dirt and super small). The beach was amazing but it's the same beach we visit in Silver Lake.