Well, the big one seems to be
Camp-A-Way, according to Woodalls. Best in the State, they brag. They have
everything. And 5 "W"s, (Woodalls best rating) to back it up. A lot of facilities though, which doesn't jive with your quiet shady thinking.
www.campaway.com 93 total sites.
Check out
Pine Grove RV Park, in Greenwood, NE
www.pinegrovervpark.com Greenwood is something like 20 miles away from Lincoln, though. 100 sites total.
At the other end of the spectrum, there's the
State Fair Park Campground which is big (199 full hookups, 349 sites total) and sounds close to town (14th St. & Cornhusker Hwy.). Under "additional Facilities", they list ice and Tenting available.
Maybe that's more what you're after. Call them at 402-473-4287
Might be fun to spend some time at each, just for a change of pace...
Good luck!