Mt Rushmore is open and has a pretty, accessible trail to the base where you can take a stroller.
Custer State Park -drive wildlife loop and Needles Highway
The Mammoth Site in Hot Springs Natl, Natural Landmark -- excellent and unique
Wind Cave NP -- open, tours running
Jewel Cave Natl Mon -- open weekdays with tours running
Journey Museum in Rapid City -- regional history and geology, open daily (Sunday is afternoon only).
Badlands NP -- about 90 minutes from Mt. Rushmore. Park and visitor center open. Rangers will point out where the herds are (buffalo, bighorn sheep).
Minuteman. Missile NHS -- next door to Badlands NP
Looks like forecasted weather is highs in 50s and 60s, lows in 30s. Might change as the date gets closer. That said, spring weather is variable. It was in the 60s on Saturday and it's snowing today, forecasted a week ago. Rapid City and Badlands NP are often warmer than Mt. Rushmore due to elevation difference.