July will be my wife and I's first time to Japan. We have the option to stay in Nishishinjuku (HR), Roppongi (GH), or Toranomon Hills (Andaz). We have 4 nights. We are comfortable with subways and can afford taxi's if needed. Enjoy good food and learning the "city vibe" in general. Usually a business traveler but this will be a holiday. We may be jet lagged first day or two, if that makes a difference. HR is very cheap which would be a good use of points/free nights, the other two are a wash but seem considerably nicer but it other areas. So I know that much... I wanted to ask those of you with experience staying in a few different parts of town at these properties if you have any strong opinions. Where would others recommend for a stay between these three neighborhoods?

Thanks in advance for your thoughts!