EDIT TO ADD: I just realized most of you won't give two hoots about this post.
Sorry about that!!! Tom, this one's for you!!
We had been to Tokyo in 2008 and on that trip, we did a number of the "big" tourist type things... Tsukiji fish market, we went to the 5th station of Mt. Fuji (which is basically about halfway up), Hakone National Park, rode a bullet train, etc... So this trip we wanted to try to not repeat anything at all, which worked out great.
For example, one of the drawbacks of Mt. Fuji is it takes quite some time to get there. So this trip, we climbed Mt. Takao. It's about 45 minutes outside the city by train, which is easily do-able, and which takes you through different parts of the city you wouldn't see otherwise. At the base of the mountain is a small village with all sorts of cool food booths, and trinket shops, and the like. Really fun shopping. There's a ski-gondola ride you can take about half way up (which was great, and freaked out the kids), and from there it's about a 45 minute hike through shrines and temples, and forests, and amazing views. There are even a few small restaurants carved into the mountain side that you can stop at for noodles or what have you, as well as small vendors selling SNACKS (I know of your affinity for those!). There's even a monkey park along the way. And that's just on the path we chose. I believe there are 6 paths, all of which provide a different experience. One walks past waterfalls. One crosses a huge suspension bridge. That kind of thing. When you get to the top, when you look one direction you have a CLOSE view of Mt. Fuji, and from that same spot, if you turn around, you have an incredible view of Tokyo. It was absolutely worth the afternoon. I could imagine a shutterbug like you going NUTS.
Other than that, we went to Harajuku on a Sunday morning to see all the teenagers dressed in cosplay and check out all the trendy shops and eat crepes (it's what they do there... There are probably 20 crepe stands). We blinked and had been there 3 hours. Harajuku is where the Olympic village was in 1964, so the main stadium is nearby, plus a HUGE park with a massive shrine. We walked through it, and stumbled across a traditional Japanese wedding procession which was incredible to see.
We went up SkyTree Tower, which was incredible.
We spent a day in Ueno Park, which is where they have the Cherry Blossom Festival every year. We were about two weeks to early for that, but they were setting everything up, which was cool to see. Also in that park is their Zoo, which we spent a few hours in and our kids loved. They have pandas, but it was closed when we were there.
We ate at a lot of good restaurants, but I wanted to find a "fun" place for the kids... So I did my homework and found Ninja Asaksa, a ninja themed restaurant. It was a lot of fun, and one of the highest rated restaurants in Tokyo. To get to your table they lead you through all these secret passages and over secret drawbridges to your little private room that looks carved out of stone. The food was very high end, but also very dicey for a Westerner. We tried it all, but only probably ate half of it.
It was a blast, but WAS NOT CHEAP. For 5 of us, it was $450.
We did plenty of other stuff... For example we spent a good amount of time in Odaiba... But what I've described here are the things that I would recommend to anyone visiting Tokyo (if you haven't already!!).
The country and the people are just amazing. Wonderful. And those aren't words in my daily vocabulary. But there's just no other way to say it. Our 17 year old has said over and over that if she spoke Japanese, she absolutely would live there for a while when she gets out of school. And I believe her. Heck, I probably would too, if it were feasible.