First off welcome home. I live in central Nebraska west of Broken Bow. Deer numbers throughout the state are really high, we haven't had an outbreak of any of the diseases that can wipe out the population. It's been about 6 years since blue tongue really hurt the whitetails. As you know Nebraska doesn't manage for quality so that hasn't changed much although we are seeing some very good whitetails especially around the Platte. As you probably know more and more land is being leased or purchased by big money a California contractor just purchased some of my best whitetail hunting area. When you establish residency apply for elk right away there is always a chance and they are taking some huge bulls south of North Platte and also the Northwest. You can draw an antelope tag every 3rd year as it usually takes 2 or sometimes 3 points depending on the unit I usually hunt Wyoming as antelope in Nebraska still don't have the genetics and lush grass evidently doesn't grow big antelope.
As far as bird hunting turkeys have had a few bad hatches but still plenty around, the obvious limiting factory is private access if you're moving to a rural area you should be able to get access if you meet local people, if you're coming into a metro area it will be harder. Pheasants in the southwest are really doing well It opens tomorrow central part of the state is still down some from 10 years ago because of lack of habitat. Grouse and chickens it is a down year but I've already shot 20 or so.
The Huskers are terrible but better times are coming. Welcome back and good luck and if you want to PM me with any specific questions feel free to I spend a lot of time hunting throughout the state.