I worked there a few years ago, I can say that the usual "touristy" things are quite good, but even just walking around Tokyo itself is pretty fun. Akihabara is a must see if your into the anime culture and games, as is Shibuya especially at night. Night time also brings out some of the best sights for the Tokyo Tower and Rainbow Bridge, especially if you go up to the top viewing deck. The night time views of the bright lights of Tokyo can be stunning.
If your an early bird, get up real early, maybe 4am, and head to Tsukiji fish market. You'll be amazed at the amount of fish and even try out the freshest sushi in the world (if you like that stuff), nothing says fresh like just pulled out of the ocean an hour or so ago. Though be warned that it is a working fish market and can be very busy and hectic.
Asakusa temple is also a good visit, if you get the right day there is also a kind of flea market around it where you can pick up arts, crafts, gifts and DAMN GOOD food for very decent prices.
Siightly further out of Tokyo (maybe an hour by train) you can visit Nikko, which is basically a giant shrine and temple complex. You can get there from Asakusa station in Tokyo and is a good day out. In the same area is a theme park called "Edoland", I'd look it up before you decide but it is a tonne of fun with friends.
Just enjoy yourself over there, I can honestly say that it was the safest place I had ever lived/visited in my life, and I've done a lot of travelling. I will say one thing though, if you can, AVOID an area called Kabukicho. This may sound like fiction or wild tales, but its basically Tokyo's crime/gang land area. According to Kurumi, the girl I was living with, its an area of high Yakuza influence and presence and they often like to prey of western or out of town visitors. I avoided it like the plague, so thats just a handy word of advice.
In terms of Kyoto, there are a LOT of shrines/temples there. The obvious ones are the Kinkaku-ji (golden temple) and Ginkaku-ji (silver temple), well worth a look. The Gion district is also worth a visit, real life working Geisha wtill walk the streets and there are other ones you are allowed to photograph. Feels a lot more traditional than the rest of Kyoto. Outside of Kyoto theres a place called Fushimi-Inari, another temple complex but one of unique visuals. I hope you like Torii and stairs, because that place certainly bloody does.
I will recommend looking into the Japan Rail Pass for your trip, they can be a little expensive on the surface but by god are they invaluable once you are over there. They allow for use on all trains, at any time, both local lines and the Shinkansen (bullet train). Really is worth looking into if you dont want to restrict yourself to just the inner cities. I can also recommend a handy little app for you, "Hyperderia", will give you detailed times and places of trains and departures. Really really does come in very handy. I'm gonna leave it now because I'm starting to seethe with jealousy and nostalgia. I hope my ramblings are of some help. While the places I've mentioned are great sights to visit, you can usually find some interesting things by just walking around and stumbling into things. But if you are over 6 foot tall with blonde hair and blue eyes, be prepared to get stared at....a lot......by every age.....and waved at by girls.............no matter how young :S