Residents and non-residents are required to buy habitat stamp in addition to archery deer permit. On-line is easiest way to get permit; this way you can wait until you're sure your going and get it right before you head out the door and you do not have to find a NGPC office to stop in during business hours once you're here. Next year, for the first time ever, the standard archery license will be good through the nine-day firearm season as well. But during that time you'll need to wear blaze orange so be aware of that.
My brother lives in the SW part of the state and says the same thing others have here: in that part of NE during the bow season you're likely to see more NR plates than resident plates and most will be from CO.
NE does NOT have an abundance of public ground, but I'm not sure what is available is hammered much during most of the early archery season. If anything, I'd guess most spots are underutilized until right before rifle season. During rifle season? I'd not step foot anywhere near public ground in this state.