We make 2 trips a year to the UP to pick up our son at college in Houghton. For variety we stay at different campgrounds each time we go.
We stayed at a private CG by Seney wildlife refuge. Had a great time, took a canoe trip, biked in Seney to see bald eagles, snow geese, trumpeter swans, etc. Not much else around it.
We 2nd the city park just west of Munising. Close enough to town to see Pictured Rocks & other sites. Some sites on right on the water. There is a NF cg justt west of there also.
Near Houghton we have stayed at the city park on the river/canal (no restrooms), Baraga before you get to town, McClain SP on the lake, further north at Ft Wilkins in Copper Harbor, along with Lake Michigan SF CG along US2, Straits SP in St Ignace (our preference for going to the island - less crowds), Indian Lake SP, Muskalonge SP, Soo Locks CG, and the casino in Christmas. McClain is nice due to the great views. Ft Wilkins is a long way from anything. In the Houghton area take a mine tour at Quincy. The Porkies are maybe 2 hours from Houghton. We are planning on going there this fall when we drop him off back at school. Another park not mentioned is Fayette on the south side on the shore of Lake Michigan. Neat old iron ghost town. Beautiful harbor.
My recommendations on what to see - Pictured Rocks (take boat tour), Seney (drive, bike ride, or canoe), Kewanaw Pennisula & Copper Harbor, the big spring, Fayette, and the Porkies.