Considering a drive out to the Black Hills region (from Cincinnati) for our family spring break this year. Long drive but hopefully worth it?! We'd likely arrive the evening of Friday, March 30 and depart Thursday, April 5. Three things I'm wondering: 1) Chance of snow/inclimate weather this time of year, 2) How to divide our time seeing the various sites, 3) Where to base our lodging in the area. We have two adults and three kids ages 11, 14, and 15.

March and April are multi seasonal and you should expect anything from a blizzard to warm spring days. Every year is different.
It is hard to give any recommendations without knowing some likes/dislikes?

We'd be interested in sites such as Badlands Ntl Park, Mt Rushmore, Crazy Horse, Custer State Park, caves, Wall Drug, etc. Love to hike. Don't like hearing the blizzard potential though...

1) When staying in the Black Hills area, the small towns of Hill City, Custer or Keystone would be the most centrally located to most attractions/sites. Restaurants/lodging/shops
in each. Lodging is also available within Custer State Park at several different locations, but dining only within the lodging area.
2) SD Badlands are about an hour East of Black Hills - can easily be driven/hiked in a day. The rest of the days could be divided seeing Mt Rushmore (they also have a night lighting), Custer State Park, Wind or Jewel Cave, Mammoth
Dig Site/Museum, etc. You could easily see at least these four attractions, and more, as the area is easy to drive; mostly in a loop.
3) BUT....Summer/Fall is a better time to go. Some lodging/attractions may still be closed then, and the weather definitely can be "iffy". Even if it's a nice, sunny day, you'll still need a coat as the wind will have a nip to it. And if it's not, you'll need an even thicker coat & a shovel!! Blizzards are usually done by then, but you never know..if it snows & the wind comes up, there you have it!

If you decide to go for it, I would call ahead to Black Hills Area Tourism to see what is open/closed, including park roads. Mt. Rushmore is open year-round, but not sure about all the other attractions. It would be a long way to drive to be disappointed with site closures.