Honestly I don't like Tokyo much, if you're interested in more historical sights you'd be better off traveling more from location to location via Japan Rail. I can name a couple city with some beautiful historic sights worth seeing, authentic samurai castle, temples, the full deal, even give tips on the Japan Rail and the like. Fun times! And if you've gotta stick with just one city, I'd actually preferred Kyoto. But then I'm just not a fan of crowds, and Tokyo is insanely crowded.
Nevertheless... Tokyo eh? Well I enjoyed the Meiji Shrine and its surrounding park and gardens, very impressive. Especially early in the morning before things get all crowded as they have a habit of doing in Japan. Senso-ji Temple is pretty neat the first time you visit it, even if it is a bit, erm, touristy. But then the hotel I was staying at when last I was there was literally right next to the place so I got kinda used to it!
Just wandering the streets was probably the most entertaining thing to do I found though. It took me awhile to find it since I got hopelessly turned around, but Yanaka District made for a fun walk and it felt much more, how would you say it... cultural since unlike most other district, there are a fair number of original houses remaining there that haven't been replaced with cold concrete boxes. The Ameyoko market was another fun walk, never actually bought anything aside from the occasional snack, but it was alright. Ueno park nearby is worth a look, but I was underwhelmed. Tokyo National Museum is in Ueno as well, but again, underwhelmed. Fun to visit for sure if you're a history buff, but not somewhere I can see myself wanting to visit again. And of course you've gotta do at least one trip to Daiba. I don't even like anime, and I know about it. The TV studio there is massively impressive and there always seemed to be something going on, arcades, modern malls, plus there's a giant Gundam statue... or at least there was when I was there, not sure if that was a permanent thing or not.
And then there's the gardens. Perfect to relax in after the hellishly crowded streets of Tokyo. Korakuen Garden and Rikugi-en Garden were the two I enjoyed most. Both only let down by the unfortunate fact that they're essentially gardens of tranquility amidst a sea of humanity, so the sounds of vehicles, planes, yelling and shouting are never far off. Neither I found all that crowded compared to the rest of the city, it was nice.
And of course there's Shibuya, Roppongi & Akihabara, which as I understand it are 'the' places to go. I didn't like em, but perhaps you might. Shibuya is shopping, Roppongi clubs, and Akihabara anime stuffs. Akihabara is the place you wanna go if you're into seeing grown women wandering the streets dressed like cartoon maids (advertising) with men standing nearby with a loudspeaker shouting incoherently (more advertising) while waving towards a giant poster of a barely covered anime girl (yet more advertising!). Heaven itself I've been assured if you're into that stuff, which I suspect you are what with the av and all, but I just found it loud, noisy, and confusing. Go figure! You'll probably have better luck!
Oh, and be sure to ditch Tokyo at least for one day and visit nearby Kamakura as well. Close enough it can be a day-trip. Tons of temple and monument, huge buddha, all very impressive. Still crowded though, since it's so close to Tokyo.
Good Luck!