Stay at the State Game Lodge in Custer State Park if you can get in. Odds probably aren't great for that time...but look into it. In Hot Springs itself Red Rock River Resort is probably the best place to stay. I'll be honest, Hot Springs isn't a great town. I'd recommend staying in Custer, Keystone, Rapid City, or Hill City in the Southern Black Hills... you can also look into renting a cabin. If you want to stay in downtown Rapid City and have a little bit more access to food and nightlife I recommend the Hotel Alex Johnson or the Rushmore Hotel. If you can find a room in Keystone that night, the fireworks at Mount Rushmore are probably second only to the Statue of Liberty.