The Boise airport is small, and you'll have to leave the concourse areas to claim your snowboard bag.
There are very few, if any, suitable places to "camp" outside of TSA secured areas. Most of this area is open and brightly lit with tile flooring. The possible exception might be the greeting area for arriving passengers just outside of security.
There are several budget hotels within short walking distance of the airport. Most offer free 24/7 shuttle. Google Maps will give you a good idea of what's available.