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!

There's many threads on this, but here's a brief summary. I've stayed at all three.

- HR is in an office district in Shinjuku. Not the best location, fairly quiet and a bit of a walk to the actual station but like you said a good value especially on P&C.

- GH is in Roppongi which is the most foreign friendly neighborhood and the best location. You will find the most English speaking people here. Lots going on in terms of bars, restaurants and city vibes.

- Andaz is a few minutes (5min cab) from GH and a much nicer property though slightly less ideal location, however still very well located and close to the Toranomon subway line. You will have to take a connection to get to the JR which is worth considering if you plan on using the trains a lot.

Most would opt for the Andaz, you might also consider splitting your time between GH and Andaz as they're close enough that checking in and out shouldn't be a huge hassle.

I would go for the HR in Shinjuku for a first time visit. You cannot really go wrong with all choices, but I like the Shinjuku area the best. And to say that it's an office district is not completely accurate, there's a lot of other things to see and do within a few blocks.

You might get more luxury elsewhere but for me the HR is still hard to beat as a tourist.

+1
It was also my choice for 1st time, 2nd time was PH, 3rd time GH, 4th time Andaz.

If you like walking, the Andaz might be fun as it's a long but pleasant walk to the Imperial Palace area and Ginza. In the other direction, you can walk to Tokyo Tower. It's in an upscale residential area with new high rise buildings, including the hotel itself in a mixed use skyscraper (some food and limited shopping, office space, residential units, and hotel space, including a spa).

Sorry to sound sceptical.... but you mean it's located in a moder skyscraper that could be located anywhere :-). And I do like the Andaz, but for a first time visit.....

Not sure what advantage you think HR offers for "first time visit"? Are you implying the majority of things a first time visitor might want to do are in Shinjuku?

It simply depends on how much time OP plans on spending in/around his hotel room.

AFAIK all of the Tokyo Hyatt properties as well as most of the (especially western chain) hotels in central Tokyo are located in modern skyscrapers, so this shouldn't disqualify the Andaz unless the OP is considering staying in a traditional inn.

Roppongi is the most foreigner friendly, but mostly for the bar / restaurant scene. I wouldn't necessarily want to stay there, just take taxis in and out for dinner.

Shinjuku is a very convenient transport hub, as well as near some of the interesting sites (Meiji Shrine, Tokyo Metropolitan Building viewpoint, etc.). I quite like staying in that part of town.

Since you get 2 nights at the HR on points for the price of 1 at the GH or Andaz, why not stay 2 or 3 nights at the HR and 1 or 2 at the iconic Park Hyatt? It's a short walk or cab ride between the two.

P.S. Walking around Ginza, Shibuya or the east side of Shinjuku station at night when jetlagged is great for sensory overload. I feel a bit cheated when I'm in Tokyo but sleeping normally.

That's my sentiment as well... I find Roppongi to be somewhat of a sleazepit, where I cannot walk in the evening without being talked to by some pushy Nigerian. Not the Japan experience I'm looking for.

But yes, none of the Hyatt properties will give you much of a local feeling. The Andaz and the PH are by far the most luxurious so for free nights or points probably the best choice.
But if you plan to pay and spend most of your day seeing the sights the HR is a great value in a nice area.

Yes, the homeless all over Shinjuku are much nicer.

Only in the park at the back and sometimes under the overpass..... not areas I tend to spend much time. And the homeless don't bother me.... those Nigerians do.

But I get it.... the Andaz rules.