I live here and can tell you that on public land the hunting is not that great during rifle season. Lots of pressure and not a lot of land. The tags are cheap but not unlimited for nr's. Most areas have been cut back in recent years after all the die off.
You also get a lot of residents from the eastern side of the state who will shoot the first forky mule deer they see.
Not trying to discourage you but with easy to get tags, cheap tags, and the fact that you can shoot 2 bucks a year Nebraska is not managing the herd for quality.
There are plenty of better tags out there. Just about any region in Wyoming will offer better opportunities for mule deer IMO.
If you want to hunt Nebraska go bow hunting right before gun season starts. That is the best time of year IMO. The second best would be archery hunting the opener in September. You can get a public access maps on the website and they have a free downloadable app for your phone that includes maps and all kinds of other options.
That being said there are some whoppers out there. I know a outfitter in Hay Springs that kills some whoppers every year.