We live in Frankfort, about 30 miles from Traverse City. We stay as far away from Traverse in the summer during Cherry Festival because of the huge crowds.
Traverse City has a TON of stuff to offer as far as tourism, nice beaches, shops, and restaurants. (for that matter, so does Empire, Glen Arbor, Sleeping Bear Dunes National lakeshore, Frankfort, etc)
Some places to camp:
Interlochen State Park
Cherry Bend RV resort in Lake Leelanau (quiet, fair amount of rules)
Airstreamers campgroumd near Chum's Corners on the outskirts of town is OK.
I have not camped at the TC State Park
There is a KOA, we've not camped at either.
Platte River books VERY quickly, is super popular.
Sleeping Bear Dunes does have camping, too....
Hope that helps, you're welcome to PM me if you need anything else.