Wow - it sounds like you're having a "Lost in Translation" moment (from the movie), where you're in the world's biggest metro area yet feel strangely alone and disconnected from people. Tokyo can do that to people in its own unique way.

Others have made some great suggestions already. Let me add some:

- Yokohama, specifically Chinatown. Yokohama has a somewhat different vibe than Tokyo, and Chinatown has a totally different vibe. If nothing else, go down there for lunch or dinner one day, and spend an hour or two wandering around.

- Mori Museum in Roppongi Hills. It's one of my favorite museums. It has no permanent collections, but displays one major and one minor exhibit at any given time.

- Edo Tokyo Museum. See the history of the city of Tokyo over hundreds of years.

(also, I should say that I find "art museums" in general to be among the most boring things in the world, but I would make the two above recommendations even to those people that generally don't like museums)

You said that you're not interested in drinking. I'm not sure if that means you don't want to go out and get hammered, or if you don't drink alcohol at all. Even if it's the latter, don't rule out going to a bar or nightclub. You can have a fine time just having a drink or two without overdoing it, or even just a soft drink if you really don't drink at all. Here are some ideas:

- Go to the bar at the top of the Park Hyatt in Shinjuku. If you're going to have a Lost in Translation experience in Tokyo, you might as well do it where the movie was filmed . Don't just stop at the upper lobby bar - continue thought the hotel up to the New York restaurant. Go before the Y2000 cover charge kicks in, which was 8pm the last time I was there, and it will only cost you one drink to have the experience.

- Go to a "live house" as someone else suggested. Kento's is a chain with 4 locations that has cover bands often playing oldie American songs, like from the 50's and 60's. It's interesting to see the Japanese audiences get really involved in it.

- Because you mentioned difficulty in speaking with locals even after trying, try going to a bar or club that's known for having a lot of foreign clientele. And these are not all dives in Roppongi. I might recommend Hobgoblin in Shibuya. It sometimes has live music and sometimes not. But all of the staff will speak English, and there will be a lot of foreigners there. Plus, many of the Japanese customers will be able to speak English. You'd probably have better luck striking up a conversation there sitting at the bar than many other places in town.