In the old days of the DLH, the Monorail used to dock right there on the DLH property. Now, it departs from its station in DTD, takes you to Tomorrowland and then comes back to DTD.
If you thought the walk from DLH to the gates of the parks and back was a bit much, then you most likely would not like the walk to and from the PPH, which is across the street from the main hub of activity. Even though by taking the "short cut" to and from the PPH (going through the GCH lobby), the walk will be ever so slightly shorter than the walk from the DLH, it is not too much shorter. Really, the 'closest' hotel is the GCH in terms of proximity to the gates of both parks (and it has its own entrance to DCA), BUT it is very, very expensive (more so than the DLH by a mile!) AND you are not guaranteed to get a room that puts you near any elevator, therefore making the walk to get to an elevator a rather long one, thus negating any anticipated saved footsteps! So in other words, if you ended up with a room in the GCH that was way down the endless corridors, it would be almost the same as walking to and from the DLH or the PPH, roughly.