I assume you'll already have bought Japanese currency and arranged for accommodation so wouldn't the first obvious thing to do be travel to wherever you'll be staying in?
Japan is about as different from Europe as the US is different from (non-English speaking) European countries, at the least.
My first thing was, after going through customs, money exchange, and buying a snack and a cola from the kiosk. I got on to the Narita Express and took it to Tokyo, I got off at Takadanobaba station, and switched to the Seibu Shinjuku line, and went to my hotel.
Bitched and moaned about how they broke the zipper on my bag/backpack (2 seperate bags that USED to be able to zip together), bought a melon soda, then walked around Shinjuku in awe I think, before going to the traditional style inn in Saitama. I swear I was on such a natural high the whole time.
ran to try and get through Immigration and customs as quickly as possible and race down to try and catch the first train (usually the Yokosuka line) before you had to wait another hour to get out of Narita...
Getting out of Narita was always a pain..if you didn't want to spend bundles of yen using their express line.....
The first thing I did when I got off the plane and first stepped foot on Japan about 10 years ago is (THIS IS THE HONEST TRUTH) I kissed the ground and screamed "I'm FINALLY HERE!"
After getting a bunch of strange looks then I went straight to my hotel and passed out.