If it is a long walk from the HR to Tochomae station, then it must be a marathon to any of the stations from Andaz. Maybe with a stroller it is easier to cross the street to the gov building because there is an elevator there, but we usually went down to the basement of the HR and accessed the station from there, maybe 2 minutes?
I'm absolutely sure that the HR is the closest and most convenient to a subway station, especially if it is raining or in the heat of summer. That said, once on the Oedo Line anyone is most likely to have to change at least once and often twice to get to most anywhere.
In good weather the walk from Andaz would be fairly easy with a stroller (maybe less so with a 2-yr old walking), and the different lines available offer more options for taking the trains with fewer changes. On our last stay at Andaz we ended up using Uchisaiwaicho Station a lot; it has good elevators and for some reason it often worked out best for where we were going. The opening of the Toranomon Hills Station on the Hibiya Line next year will make Andaz even more convenient.
The GH is pretty close to the station, but I remember when leaving we wanted to go back to Tokyo Station and with luggage it was a bit more of a walk to an entrance with and elevator; it has been a few years, so maybe that has changed.