I've hunted public and private in NE almost every year since '08. There was a huge die-off from blue tongue and EHD in 2012 and to a lesser extent in 2013. In 2014 there were tons of fawns running around everywhere and good numbers of 1 1/2 year olds. Bucks in the older age classes are very few. While the impacts are localized (some areas were hit harder than others) I still believe if you give it a couple of years to recover, then you will have a much better hunt if you are after a mature buck. The Northwest part of the state has the highest concentration of public land. Oglala National Grasslands, Nebraska National Forest, Valentine National Wildlife Refuge, Samuel R. McKelvie National Forest, and Crescent Lake National Wildlife Refuge are all open to hunting. Ft. Robinson state park I believe is open to hunting, as are other state lands, WMA's and walk-in areas. The walk-in areas change from year to year so be sure to use the most up to date info from NE Game and Parks. Because of recent drought (12-13) they have allowed some areas of CRP to be hayed or grazed thereby reducing critical cover, so some walk-ins might not be as productive as they once were.
The whitetails in the areas I hunt are already recovering nicely and based on the numbers of fawns I saw last year the mule deer won't be far behind. If you just want any mule deer buck give any of these areas a try. Otherwise I say about the fall of 2017 there will again be a high number of bucks in the older age classes to hunt.