Unlike any other big city in the world, people talking to some one who sit next to he or she, people smile to each other some one you don't really know, people saying hi to each other, but in Japan almost no one doing this. Not even for the Japanese, amongst the foreigner vs the local, most of the time foreigners has really hard time to know the local Japanese, in order to change this, the best way is through any society or club or organization. The fact is, this involve a lot of money for the membership.
So, I suggest you to join any government built sport club as you don't need to pay a big amount of money, besides, you can easily make friends or even you life partner. Who knows?
If you like skiing/snowboarding, consider a trip to Ski Dome SSAWS, an indoor ski facility in Chiba near Tokyo. Pronounced ZOUSE (rhymes with HOUSE), SSAWS is a year-round, completely enclosed ski facility. If you take the bus from Narita airport to Tokyo, you'll pass the large gray structure on your left.
The main attraction is its pure novelty. Especially if it's the middle of summer. It may be 40C outside but you can still say, "Hey, let's go skiing!" You don't have to bring anything, everything from equipment to clothing can be rented. I don't recall the prices exactly but expect to spend anywhere from Y5000 to Y8000.
Also expect many beginners on the slopes. Of course weekdays are recommended as they are less crowded. Ski and snowboard times alternate and are mutually exclusive so check the schedule ahead of time if you don't do both.
The longest run is 500m in length with a vertical drop of 80m. Half the width is split into an advanced slope. The other half is an intermediate slope, and halfway down the intermediate slope is the beginners slope. Two lifts and one 'escalator.'
By the way, if you're in the neighborhood and just want to take a look without skiing, there is a cafeteria overlooking the slopes. I believe you still need to pay some small admission fee to get in, however.
There are some good pictures on this web site: http://www.emit.com/jurgen/japan/jp1998020101.html. Also, a good intro and pictures of the facility are here: http://www.aircrewlayover.com/Cities/NRT/Ski_Dome/ski_dome.html.
Location: Minami-Funabashi station on JR Keiyo line. About a 30 minute ride from Tokyo Station (and a 10 minute walk to the platform within Tokyo Station!)
BREAKING NEWS: SSAWS has closed and it is no longer possible to ski here...
See Sumo without sitting through hours of tedious salt throwing and stare downs! Don't pay outrageous prices! See the famous wrestlers up close! It's called Asa Geiko (morning practice). There is none of the boring salt throwing and stare downs that you have to sit through during the tournaments, and you don't have to pay 30 000 yen for a front row seat--you just have to get there early (8am at the very latest). You can see all of the famous names up close and personal, and some of the friendly ones will even pose for pictures. After several hours of warm up and technique practice, they play an exciting 'King of the Castle' game where one wrestler stays in the ring fighting bouts without any rest until he is defeated.