Aside from the private airport in Alpine the closest major airport is in between Midland/Odessa. Approximately 2 hours and 15 minutes from Alpine.
The next closest airport is in El Paso. Approximately 3 hours from Alpine.
If the venue lodging is at maximum capacity and still need a place to stay
We highly recommend the Bienvenido Big Bend bnb's!
Check out their website at www.bienvenidobigbend.com