Nebraska is pretty good if you find land with varied topography. My family has a homestead near Chadron, in the panhandle. The area used to be booming with outfitters ten years ago, but the economic crisis combined with a blue tongue epidemic did most of those operations in. Today, I imagine the deer populations have re-stabilized (but the outfitters mostly still gone), and you might consider calling some ranchers to see if they'd let you hunt for a couple hundred dollars.

One of the nice things about the northern part of the panhandle is the overlapping territory between mule deer and whitetails. I tend to find the whitetails prefer creek bottoms and cover, whereas the muleys don't seem to have qualms about going out into the open. The two species are crazy territorial, and wooded cover seems to be a porous dividing line between their ranges. I just can't speak to the quality of public land, but there seems to be plenty in the far northwest of the state:
https://maps.outdoornebraska.gov/PublicAccessAtlas/