Aside from going to see an actual tournament, one thing which I highly recommend anyone visiting Japan to do is visit a sumo training session.  I saw a practice at former "heart-throb" 力士 / rikishi (wrestler) Terao's 部屋 / beya ("stable").  I was blown away by hard these guys trained, as much of the practice was taking turns doing several consecutive, explosive bouts with each other wrestler, any single one of which would seem enough to wipe someone out for the day.

Here are some other aspects about sumo which are also interesting:

1. Sumo's origins as part of religious (i.e. Shinto) ceremonies and celebrations for the rice harvest.

2. The less glamorous aspects of sumo (especially for younger wrestlers).

3.  "Cooperative corruption" between wrestlers and "stables" (pretty much generally known in Japan, but seldom mentioned in polite conversation.)

4. The rikishi's bread and butter: Chanko-nabe