An amusement park takes up a large part of this area. Rides seem to hang over the city streets, and they actually go through buildings and each other! They can all be ridden separately, or an 'all you can ride' pass can be purchased. The amusement park is built into the Tokyo Dome City, so it is free to walk around the rides.
Built halfway around the amusement park is 'La Qua', a building filled with over 70 shops and restaurants. There is also a natural hot springs spa built into the upper floors.
Towering over everything is the 155 meter Tokyo Dome Hotel. I recommend having the buffet lunch at the 'Artist's Cafe' on the 43rd floor. Named after the artists that perform in the Tokyo Dome, make sure you reserve ahead of time to get a table right by the window. The city views are fantastic! If you are in the area at night, stop by the bar for the same great view, often with live music performances.
Also within the Tokyo Dome City is the 'Japanese Baseball Hall of Fame and Museum' (see next review). The Tokyo Dome itself hosts over 60 baseball games a year, as well as a number of other sporting events (boxing, American football, monster trucks,...). There are also special exhibitions, the most famous being the yearly 'International Great Quilt Festival' held every January (photo below).
The Tokyo Dome City also contains the largest JRA WINS horse race betting complex in Tokyo. Here you'll see many down-on-their-luck Japanese men hanging out, smoking heavily, trying to win their way out of disfortune. A large game center is beside WINS, in addition to games there are batting cages, bowling, and more.
For English information on everything I've mentioned, visit this site: http://www.tokyo-dome.co.jp/e/dome/
Access: Tokyo Dome City is located in the southwest corner of Bunkyo Ward. Korakuen Station (on the Marunouchi and Namboku Subway Lines) and Suidobashi Station (Mita Subway Line and JR Chuo Line) puts you right in the center of the 'City'. It is also a very short walk from Kasuga and Iidabashi Stations. Here is a nice map of the area: