It all depends on how much effort you wanna put in. Public in Nebraska gets pounded just for the reasons you stated (unlimited, cheap NR archery tags). It’s the first state you can OTC hunt mule deer. I could retire if I had $1 for every MN, WI, PA, MI, plate I’ve seen.
That said if you are willing to hunt sun up to sundown, cover more ground than everyone else, and be happy filling a tag and not trophy hunting it’s a doable hunt. Just remember its not a mountain “back country” adventure you’ll never get away from people. Your best bet is to avoid weekends, holidays, and opening week.
The Sandhills are very weather dependent, plenty of summer rain and there will be scattered pockets of vegetation where deer can bed up and its a run and glass game. Drier years will concentrate deer in the low areas, but most decent vegetation will be on private. There been times over the years I’ve been into good bucks for days on end and punched tags early, there’s been years where I don’t think I coulda found a deer with a helicopter. If you wanna be up 2 hours before light, hike in, put miles on, and show up back to the truck an hour after dark you’ll do good and learn a lot. If you wanna do what 90% of people do which is drive around all day and put on 1/4 mile of walking…….. well our G&P appreciates your donation and be sure to tell everyone else there’s no deer here.
Edit to add: remember your tag is good for the entire state. Don’t waste all your time hunting a place with no deer. An hour or 2 move can make a huge difference.