In cities I like parks, museums, architecture and I enjoy walking through cities to explore.
I'm also a geek, so anything that is techy and worth seeing / doing will need to be investigated. I like food too!
I went there as a food tourist, and if you're up for eating certain things that are unusual by UK standards, then it'll be absolutely awesome.
Some things to try:
Torisashi - basically raw chicken
Whale - minke, and no, it's a long was off endangered (check Google)
Tsukiji fish market (rumoured to be moving, no idea if that's happened yet) - go there to see an incredible array of edible sea life, and also eat there. I would avoid eating in the restaurants outside of the market as they're really tourist traps and do not seem to sell the fresh stuff. Inside the market is where the truly fresh stuff is
Baby conger eel - very short season, so possibly not around when you're there, but they look like fat, translucent rice noodles.
Izakaya - just the name for little drinking dens, selling awesome snack food. Snack food like barbecued chicken heart, liver, battered cartilage, lots of other tasty stuff...
Finding places that serve some of the above require you to get friendly with some locals - I could not have found them without their help, and unfortunately I have zero recollection of the location of where I tried them.
Techy stuff is everywhere. Akihabara is the main electronics market. I didn't go though, so can't comment on it.