First off, you're going to Japan during the hottest time of the year. Last time I was in Tokyo in late August, it was 35+C with high humidity. Factor in the weather while figuring out your itinerary. If you're in Tokyo at the end of August, you can enjoy the Koenji Awaodori, the "farewell to summer" festival.

Japan is big enough to warrant several visits to visit different parts. First timers usually do Tokyo and Kyoto in a day or two, although with the size of Tokyo (it's the biggest city in the world), that's rushing it. The best way to tackle Tokyo is to realize that it's really 23 cities (ku) connected by rail. Each ku has its own personality and attractions. Shibuya, Roppongi and Shinjuku are different from Taito, Ota and Chuo.

Most people try to do Kansai (Kyoto, Osaka, Kobe, Nara) in the same trip. Kansai is worth it's own return visit; there's a lot of stuff there. Kyushu is the southernmost main island with its own attractions as well as Hokkaido in the north that has great dairy products and winter attractions.

First time visit, I would break it up. 4 days in Tokyo and 4 days in Kyoto. Figure out what you want to do/see in advance including lodging.

If you're looking for odd stuff to see/do, Tokyo has a lot of that. For example, tourists always hit the Tsukiji Fish Market for the early morning auctions. I go there for early morning sushi (typical) or to visit the Yoshinoya store #1, which is also at the fish market (weird). They allegedly make their gyudon with Japanese beef there AND they close at 1500. Odd like that?