How about the Big Bend Motor Inn over in Study Butte? Their
website appears to be offline (at least for me). They've supposedly been bought by Forever Resorts, which also runs the concessions in the park. As far as activities for teenagers.... Big Bend is kind of a "do it yourself" area when it comes to entertainment. Don't expect to find video arcades, skate parks, movie theaters, etc. If they're not willing to get out and explore nature, they'll likely hate it.
Big Bend Motor Inn's phone numbers used to be
Reservations: 1-800-848-BEND
Information 432-371-2218