Omaha area campgrounds
Welcome to Omaha. You'll love the Olympic Swimming venue at the CenturyLink Center in downtown Omaha.
The closest camping to downtown Omaha is at Bluffs Run Casino in Council Bluffs, IA, about 6 minutes away. I've never camped there, but have driven past the casino many times. The campground is basically an asphalt parking lot. Lake Manawa SP, an IA State Park, is about 20 minutes away and takes reservations. Unlike most of IA State Parks, the park's facilities are in need of updating and the grounds seem a bit "seedy".
Omaha is basically a 20 minute city meaning one can make it about anywhere in the city in 20 minutes. With this in mind, I'd recommend Haworth Park in Bellevue, NE and Walnut Creek Lake Recreation Area in Papillion, NE. The former takes reservations and the latter doesn't.
I hope this helps,
Rig: '97 30' Limited
Towed by: '13 Silverado 2500 Duramax