If you are coming from Kyoto by Shinkansen (Bullet Train), then I suggest that you get off at Shinagawa instead of Tokyo Station. (It's just a few minutes before arriving at Tokyo.) There may be some Bullet Trains that don't stop at Shinagawa, but most do.

Without luggage, it's 160 yen from Shinagawa to the GH Tokyo, but you have to change lines once and, as others have noted here, it's then a pretty long haul (7-10 minutes walk by my watch) from the subway to the hotel. Unless you want a workout, I wouldn't do it with family and luggage in tow. For going out later, once you've checked in, the subway is very convenient and cheap.

A taxi from Shinagawa to the GH Tokyo should be around 2,000 yen. I recently paid about 1,500 yen but that was at 6 in the morning with no traffic at all. For my money, you'd arrive in better shape by taxi.