Nebraska/Wyoming/South Dakota border area
Hello hippyman,
I took the liberty of assuming you're Texas point of departure is Amarillo, so that means US 287 to US 385 all the way to the Black Hills would be the most direct route. Departure from farther east, like DFW or Houston would bring you more through central Nebraska, but as you'll see, that's not a problem.
The US 385 route takes you through Sidney, NE, the home of Cabela's, Inc (World's Foremost Outfitter). They have a huge store right on I-80 and a full complement of goods and services are available at that exit. The town of Sidney, a couple or three miles north of Cabela's, is pretty cool in and of itself, having been founded as a railhead/trailhead for miners and camp-followers flooding to the gold mines in the Black Hills.
US 385 passes through Alliance, NE north of Sidney, and just a handful of miles to the east is Carhenge.
North of Alliance is Chadron, NE, where the Museum of the Fur Trade and the Sandoz High Plains Center are located. Just west of Chadron is Crawford, NE, location of Fort Robinson State Park. Fort Robinson is a nicely restored US Cavalry post and is well worth a visit. Taking NE 71 from Alliance directly to Crawford takes you through a beautiful section of buttes and mesas and badlands which will make you think you're in SD, Wyoming, or Montana instead of the Nebraska panhandle.
Approaching the Black Hills from farther east can include a drive directly through the Nebraska Sandhills. The Sandhills are a little-known jewel--20,000 square miles of virtually treeless grass-stabilized sand dunes up to 400' high, pockmarked with thousands of small to large lakes and marshes, and drained by beautiful clear-water rivers. NE 2 is the "Sandhills Scenic Byway" and traverses the Sandhills diagonally from SE to NW for about 200 miles from I-80 at Grand Island to Alliance. US 83 cuts a lonely path from Kansas to Murdo, SD, directly across the Sandhills, passing through Valentine, NE close to the SD border. Valentine is a county seat and home to over half of the 6,000 residents of Cherry County, a county entirely within the Sandhills. Some of the 20,000 to 40,000 acre ranches in Cherry County have airstrips from which ranchers fly into Valentine, hop into their "town truck" to fetch up groceries and supplies, then fly back to the ranch. There's a cool little museum in Mullen, NE, and flatwater paddling can be booked there, as it can be in Valentine.
Enjoy the planning the RoadTrip!
Foy