I'm going to Tokyo for a few days and will be on a tight schedule. I'm grateful for any tips on what to do, see and eat while I'm there: landmarks, sightseeing, temples, local food, sumo wrestling, markets, crazy Japanese things etc. The more Japanese, the better!
For local food, I think the best thing to do is just to walk around and find places. Look for places with large crowds, they are usually the best. There are a ton of yakitori places around Tokyo Station, which is a great treat for a beer and some grilled meat snacks. I'm not sure if they'll still be open (probably too late), but the roof-top beer gardens that department stores run are an interesting experience. You get a little grill and you cook your own food. Check out the Tsukiji's fish market for an interesting experience, and then grab breakfast at a soba noodle place or sushi joint (if you are up for 7am sushi).
For site-seeing, check out the view from the Municipal building observation deck near Shinjuku station. It's free, and as good a view as you would get at the Tokyo tower or City View (which both cost money). Shinjuku is a cool place to see - crazy busy.
Play some Pachinko.
For sumo, check out the Japan Times Sumo Schedule to see if a basho (sumo tourney) is happening when you are there. If not, I think you can go and see a demonstration, but don't have details.
For more advice, check out my Japan Trip Report from July of this year in my blog.
For more info on Japan and tokyo check out www.japan-guide.com perhaps the most useful japanese resource out there.