Rode thru Iowa this past summer as part of an x-USA trip. From Onawa to Davenport.
And I did the Black Hills & Sandhills, too. In fact, I've ridden Nebraska many times since 1987.
How much do you want to get "back there"? And where will you be starting from?
Initially, I read you home as "1A" and looked at some reference for 1A - then realized it was IA.
Crossing the Missouri on the Kerry Bridge is nice, but Omaha is "Meh" to bike thru.
The US 30 bridge to Blair has shoulders, but the stretch in W. Iowa is busy and narrow.
The Decatur bridge has a metal grate deck and is tricky - esp. if you look down.
(Plus, the hills on the Neb. side are killer for 40 miles.)
The Sioux City Bridge has great bike lanes and bike trails on the riverfront, too.
(Although it may put you too far north for your plans.)
There are three general Sandhills routes - US 20, Neb 2, and Neb 92.
US 20 has excellent shoulders, light traffic, plenty of towns, moderate exposure to the Sandhills.
Neb 2 goes right thru the middle of the Sandhills from Broken Bow to Alliance, moderate traffic, OK shoulders.
Neb 92 west of Broken Bow is stunning - pure Sandhills - zero traffic, but remote. And the longest jog north.
Depending on how much time you have - I would go as far west as Crawford and Ft. Robinson.
Then turn north on Hwy 2/71 to Hot Springs - light traffic - and Wind Cave NP - to Pringle.
At Pringle I would shift to the Mickelson Trail all the way thru the Black Hills.
(North of Rochford you can opt to switch to the parallel road.)
After you hit Deadwood/Lead, loop back southwest to US 14A thru Spearfish Canyon (!!) to Spearfish.
From Spearfish you might be interested in hitting Devils Tower NM - but that's another post.
Pic - The Mickelson Trail