I'll be in Tokyo on the 18th and then onto the Nagoya area for 2 weeks for business. I've been to Tokyo about 10 times. I haven't been to the Dome area, but it looks like plenty to do at the Dome City. You can get around town very easily & quickly by subway or train. There is tons to see, it depends on what you want to see. Temples, modern architecture, tall buildings, electronics shopping, food, museums, etc.
Tokyo travel guide - Wikitravel