GH Tokyo is my favorite Hyatt so I'm just going to recommend that one without really justifying it. I'm not sure why I love that hotel so much but everything is always just perfect, in kind of a subtle way.
HR Tokyo is fine, I guess. I moved from the GH to the HR for two nights once when I had a couple of cat 1-4 certs that were about to expire. There was nothing wrong with the hotel but it's a significant downgrade from the GH. It's definitely a lot cheaper if that's a consideration.