Oh and we stayed in the Ibis Shinjuku.
It's very easy to reach from Narita airport as the Narita Express stops in Shinjuku (it's a little daunting to find the right exit though) and easy to get back to Narita for the same reason.
The English of the staff wasn't amazing, but if you speak easy English and slow enough (it has nothing to do with Japanese of course, I have to ask the French to speak slower all the time) it wasn't much of an issue at all. The rooms were quiet and clean, there's a lot of fun things nearby and you can take the Yamanote line on the JR to get to most places without having to transfer (not Tokyo Disney though, you need to transfer in Tokyo station, but it's super easy).
And we had a fridge in the room, which was very convinient and there's places to shop for food super close by. Pretty much accros the street and around the corner.
We were in Tokyo all of the first week of September, and it was super relaxed. We had a couple of bad weather days, but at least it was a damn sight warmer than it was here in Europe at the time so it was all good.
It's just after the summer rush, so that helps.