I've stayed at the GHT several times and agree that the location is very convenient. The standard rooms are not particularly big though and are starting to seem a bit dated IMHO.

Although I haven't stayed there recently, in July I did a property tour of the Gajoen. Their base level rooms are far more spacious than the GHT and have been renovated fairly recently so feel fresher / more luxurious than the PHT. Also, the property and location has a lot of history and local charm partially owing to the fact that they've preserved part of the original hotel which dates back to the 1800's.

In terms of access, I believe they have a shuttle (best to confirm with the hotel as to schedule and availability) to the nearby Meguro station else the walk is about 10 minutes up or down the hill. Distance wise, it's not really any further from the station than the GHT is from Roppongi subway lines (Hibiya or Oedo).