Hitchcock is an awesome jewel right outside of Omaha
If you are in the Omaha metro you should head across the river and checkout Hitchcock Nature Center just North of Council Bluffs. This is one of my favorite places to camp. All of the campsites are considered "back country" but don't worry, I think the furthest campsite is about three miles.
My preference is getting one of the campsites on the western edge of the park on top of the ridge. At night you can see the Omaha skyline lit up and the breeze running through there is wonderful.
Hitchcock is smack dab in the loess hills which is one of only two places in the world with the hill formations. The other place is in China.
The trail system isn't huge because of the size of the park, but it has a lot of up and down and is a great place to practice backpacking or test new gear before you leave the plains and head to the rocky mountains for a new adventure.
When your done with your hiking, climb up to the top of the towering platform and bring your binoculars to checkout the visiting hawks and occasional eagle. Don't pass up Hitchcock Nature Center.