Both Highway 2 and 385 are very good routes both from grade changes and condition. Hwy 2 will take you through the Sandhills region of Nebraska. Hwy 385 is an obvious choice to take you into SD and the Black Hills.
This is the route we often take from Omaha (via Hwy 92 to Hwy 2) to the Black Hills. We have camped at Halsey National Forest, and at Chadron and Fort Robinson State Parks. Chadron SP is our favorite for camping because of its RV site choices and scenery. Fort Robinson just to the SW of Chadron, is historic because it exposes you to frontier life on the high plains in the latter 1800's.
Enjoy your trip!