There is no lodging within the boundaries of Theodore Roosevelt National Park, though there are some nice possibilities in Medora, gateway to the park's South Unit.
You can start your search for lodging near the South Unit by visiting the website run by the Theodore Roosevelt Medora Foundation. Here you'll find lodgings by category: hotels, motels, campgrounds, cabins and entire houses you can rent. They even have a listing for where you can board your horse.
For a list of lodging possibilities near the North Unit, check out this list from the park.