how quiet?
a pub with rooms
http://www.kirkstile.com/roomsa cottage with optional BnB
http://www.byresteads.co.uk/not been to these^
Both in Lorton which is not that far from Cockermoth or Keswick but would be a less visited location.
Most the touristy places get packed out with dam tourists and become not quiet.
also where do you want to be?
Consider
Hesket Newmarket in the north. Has a good pub.
Lorton mid west
Askham or Helton in the middle to the east, access to Pooly Brige and Penrith
The south lakes tend to by busier and not my neck of the woods.
Also consider St Bees by the see in the west and Eskdale is nice too.