Yes you can. When considering an overnight stay in Badlands National Park, Cedar Pass Lodge is the only in-park lodging option. They offer cabin rentals, and further details as well as booking options can be found on their website. For front-country camping options, the park has two official campgrounds. The first is Cedar Pass RV and Campground, a paid site with 96 total spaces, some designated for RV camping with electric hookups. Reservations can be made by contacting Cedar Pass Lodge online or by calling 877-386-4383. The other is Sage Creek Campground is a free, first-come, first-served campground offering 22 sites. Motor homes, pull-behind trailers, and recreational vehicles over 18 feet in length are not permitted. For those preferring back-country camping, this is permissible anywhere in the park, provided the site is at least 0.5 miles from any road or trail and not visible from them.