We like Chadron State park, just south of Chadron NE. From there you can drive over to Ft Robinson which is worth your time if you like old army forts..good museums and history film, etc. There is an archaeology dig out in the boondocks called the Hudson-Meng Bison Kill Bed....makes for a nice day drive, slowly, over gravel roads...look for the brochure at the state parks. and, in route, there is a restaurant that serves really good steaks etc. but stop on your way to the dig to tell them you will be back..if you want to try it. It isn't cheap, but it doesn't cost an arm and a leg, either. :)
Also, in Chadron is a Fur Trappers museum and a local museum..Dawes County Historical museum, that is FULL of old stuff.