At either of the airports you can buy a sim card to use in your phone for internet (and use google voice for outgoing calls). They are sold at convenient stores (only the tourist ones like at the airport) and the electronic shops (the temporary sim cards are only sold at the tourist ones). Haneda airport has a bic camera mini.

Man, Japan is way ahead of the rest of the world, when it comes to certain aspects of convenience.

And way behind in others. Sims are way over priced. 1Gig is $30 vs say Singapore 7Gig for $20 or Turkey, 15Gig for $15

As another example even though > 40% of users don't have a landline more often than not you can not call a Japanese toll free number (0120) from a cellphone.

There's also the issue that unlike the USA where you can't tell from the phone number if it's a cellphone or a landline, in Japan you can. Cellphone numbers start with 070, 080, or 090 where as landlines start with different prefixes. Because of this you're judged based on your number. A person or company without a landline is judged to be less trust worthy than one with. Oh, and landlines require $700 to start (though that may have been finally fixed)

...and way behind in others. Try finding a pre-paid voice & data SIM in Japan (hint: it doesn't exist due to arcane regulations - non-residents can only get data-only SIMs). Most WiFi spots require registration that require you to confirm identity via a verification email (think chicken and egg).

I hope not to drag this conversation too much down the rabbit hole, but do you have any advise about what and where to get when it comes to a data SIM, which works on a GSM phone in Japan? Validity: ca. 1 month.

I used a pocket wifi from Sakura Mobile when I was Japan - https://www.sakuramobile.jp/

They delivered it to my hotel and it was easy to set things up.

Basically the same (except I used Rentaphone, as mentioned above).