What does "boasted" mean here? What words can be instead of it? Thank you!
Often a valley 【boasted 】no inn at all, and climbers found shelter wherever they could -- sometimes with the local priest....

Question

What does "boasted" mean here? What words can be instead of it? Thank you! 
Often a valley 【boasted 】no inn at all, and climbers found shelter wherever they could -- sometimes with the local priest....

Answer

"To boast" here means "to possess as a thing to be proud of".

The valley had no inn at all, but it would have been a source of pride if it had.
The verb can usually be replaced by "have" or "possess".