The cliff house (it has no designation in the game) is located outside of Cujo's arena in the High Tower region. It appears to have been, at one time, a possible base of operations for the enactment of The Trials, as it's lone bedroom contains some destroyed communications equipment as well as the map and key intended for Michael's trial. For reasons unknown, neither the map nor the key were ever delivered.
To the rear of the house is a lift that could be used to bypass the trip up the Stone Pillars. However, the lift was inactive when this area was introduced. It appears to have power, but no means by which to operate it. It is plausible that the lift will never be implemented, due to the existence of a shelter in the immediate vicinity. However, it would be useful for players who are not near another fast travel point and wish to make the trip back up the mountain.