Holiday Park Campground (
www.holidayparktc.com) is a former Airstream-only campground located on U.S. 31. It's a 10-minute drive from Traverse City and 30 minutes to the visitor center of Sleeping Bear Dunes National Lakeshore visitor center. It also has a private, sandy beach and boat launch on Silver Lake. It's very well maintained. About half the sites are owner-occupied (including my own), but the rest are available to transients. It's booked well in advance for weekenders; but you might find a spot for three weekday nights.
Other good options are Interlochen State Park, located about 15 minutes from Traverse City and 30 minutes from the aforementioned Sleeping Bear visitor center (
https://www.midnrreservations.com/InterlochenStatePark), Platte River Campground, located within the Sleeping Bear national park (
http://www.recreation.gov/mi/platter...O&parkId=70937) and D.H. Day Campground, also located within the national park (
https://www.nps.gov/slbe/planyourvisit/dhdaycamp.htm).
In addition to being close to Traverse City, Interlochen State Park is across the street from Interlochen Center for the Arts (
http://www.interlochen.org/). There's usually a musical or theatrical performance going on there every evening; and it's a beautiful setting located between two lakes.
D.H. Day is a first-come, first-served campground with no reservations. That doesn't necessarily mean there will be sites available. Campers already there can renew each night. However, if you arrive really early and especially on weekdays, you should get in. Some of the campsites are located right next to the Lake Michigan beach, and the rest are a short walk. The campground is less than 2 miles from Glen Arbor, a very nice resort town and about the same distance from the dune climbing hill at Sleeping Bear. However, it's about a 45-minute drive from Traverse City.
Platte River Campground also sets aside a certain number of sites for drive-up campers. As with D.H. Day, the key is to get there early. Platte River is also directly across the road from Riverside Canoe Trips (
http://www.canoemichigan.com/) where you can rent canoes, kayaks or tubes for a terrific and non-terrifying trip down the Platte River to the shores of Lake Michigan. If you want to skip the river part, just drive to the end of the road and enjoy the best beach on Lake Michigan. If you get there before 10:00 A.M., you should find a parking spot in the lot. Otherwise, you might have to park down the road and walk a little. Either way, you'll be glad you went.
Platte River Campground is also a 45-minute drive from Traverse City, but it's only a 20-minute drive from Frankfort, another very nice resort town on the shores of Lake Michigan with several nice restaurants and lots of shops.
Good luck.