The Great Plains of Nebraska have some amazing state parks.
http://www.ranker.com/list/best-nebraska-state-parks/smellsrank,
Chadron State Park
Chadron - Ponderosa Pines dominate this park in a national forest, camping, bike trails, Frisbee golf.
Smith Falls State Park
Valentine - Nebraska's highest waterfall, primitive camping only, hiking is limited, fragile environment.
Indian Cave State Park
Brownville - Petroglyphs tell the history of this area on the Missouri River, modern accommodations.
Niobrara State Park
Niobrara - Nice park on the bluffs of the Niobrara & Missouri Rivers, great place for camping & canoeing.
Eugene T. Mahoney State Park
Ashland - Family aquatic center, wavepool, lodge, restaurant, great park on the gorgeous Platte River.
Ponca State Park
Ponca - View three states from overlook, diverse park with plants, wildlife, & Native American heritage.
Fort Robinson State Park
Crawford - 22,000 acres of historic, scenic land, this park has everything one could ask for. Beautiful!
Platte River State Park
Louisville - Scenic woodland park, observation towers, lodge, cabins, tepees, archery, pool, hiking.