I'd snag a DeLorme for Nebraska, but beware of weirdness on actual field relations vs that or any map. My own experience, based on lots of map study and a little bit of on-the-ground exploring, is that there are lots of roads in the Sandhills which have all appearances to be public roads but which are instead ranch roads. That said, I was told that most ranchers welcome travelers if they'll just stop by the house and advise of their presence and politely request permission to pass through and/or camp in the cottonwoods at a pothole lake or stream crossing. Also, when calling the Cherry County Road Commissioner's office to check on some specific road circumstances, I was asked "you're not planning on coming out here with only a GPS to navigate by, are you?" Seems they find folks lost and stuck on sand roads well out of cell phone range regularly. My Verizon coverage was fair along NE-2 and in Crawford, Alliance, and Valentine, but nil elsewhere in the Sandhills.
As is said above, Fort Robinson SP at Crawford (and on US 20) is a recommended stop. It's a very well preserved US Army cavalry post complete with a large parade ground, rows of Victorian homes built as officers' quarters, a 3 story brick barracks now used as a hotel, extensive horse barns and veterinarian facilities, and a nifty geological museum of western Nebraska. Fort Robinson is west of the Sandhills but is in pleasing butte and mesa country with most of the bigger buttes being forested with scrub pine.
South-southeast of Crawford is Alliance, and just outside of Alliance is Carhenge. I wish I could have been at Carhenge for the eclipse last year as the weirdness factor must have been off the hook. Carhenge was within the zone of totality. Anyway, it's a hoot to see.
Starting just east of Alliance, the NE-2 highway, named the "Sandhills Scenic Journey" begins its 275 mile diagonal crossing of the Sandhills and loess hills leading to Grand Island. NE-2 is a beautiful drive--wide two-lane with wide paved shoulders and a 65 mph speed limit, with railroad towns every 8-12 miles. Lots and lots of great, long views of the largest of the Sandhills--grass covered dunes of 300' to 400' prominence.Halsey and its Nebraska NF campground is along NE-2 and right along the Middle Loup River. Great little campground, but it's also on the coal train railway which in 2015 featured 4 to 8 trains per night blowing the whistles for the crossing for the NF visitor center/campgrounds and for the village of Halsey just a couple of miles away. If reference to Bessey means Halsey, getting there from Alliance on NE-2 would be a good way to get there.
Close to Halsey (30 miles back west along NE-2?) is Mullen, NE. At Mullen, we took an afternoon excursion floating a 5 or 6 mile stretch of the Middle Loup River. This is done in large galvanized steel livestock watering troughs referred to as stock tanks, hence the term "tanking" is applied to the activity. Not as fitness-oriented as a hike, but a good way to see some cool Sandhills countryside nonetheless.
North of Mullen, up NE 97 (paved, but rough going), is the Samuel McKelvie unit of the Nebraska NF (or maybe it's its own NF unit?). The Snake River is dammed there to form the Merritt Reservoir. At the western edge of that unit is Steer Creek CG, a primitive CG within a stand of planted lodgepole pines. In 2015 our plans changed and we did not overnight there passing through, but we studied and area for hiking and other daily activities and found them appealing.
Valentine is the county seat of Cherry County, the largest county in NE and at the center of the Sandhills. The airstrip at Valentine is home to a dozen or two beater cars and trucks used by ranchers to drive from the airstrip into town for groceries, drugstore, etc, before they fly back to the ranch, which can be 100 miles and a 4-5 hour drive away. Float trips in canoes, kayaks and inflatable kayaks are offered on the Niobrara River in Valentine.
One planning thought: I don't know exactly when upland bird season is out in the Sandhills, but I'd find out before planning a trip requiring use of campgrounds. I understand the grouse, pheasant, and wild turkey hunting draws lots of folks into the field, so some facilities might be expected to be crowded.
Lastly, and sadly, there was once an individual who posted on ExPo under the name "roverrocks". He was a Land Rover aficionado from Colorado but grew up in the Sandhills. If they can be found, some of his trip reports from the 2014 and prior time frame are excellent sources of motivation and encouragement to get out there and explore the Sandhills. The "sadly" part is that Roverrocks died in 2015 or early 2016.
Foy