I just got back from doing a very similar trip. My $.02. Skip the Metropolitan Government Building. It's just a tall building. The observation deck is kind of a dump. It's messy and unorganized. Also, Asakusa and Senso-ji (and the surrounding few blocks) are very touristy but also very interesting. I liked my time there, but if you're not into walking the tourist line, it doesn't take that long to see the temple (which is beautiful). While you're there, why not swing over to Ueno and see the park and Tokyo National Museum? You can do the entire museum in 1.5 hours. I also liked the Edo Tokyo Museum and might add it to your itinerary.
Kyoto is GREAT and by far my favorite city in Japan. Spend as much time there as you can. Kyoto station is a great place to stay - there is a hotel in the station (Hotel Gran Via) that I stayed at and was well worth the money for the time saved. Check out the ramen restaurants on the 9th floor. The Philosophers Path is WAY over-rated. Ginkaku-Ji is great and so is Nanzen-Ji. Everything in between is not that interesting (to a tourist. I'm sure it's great if you're Japanese, it's just not beautiful or awe-inspiring or anything). Also, I liked Gion Corner - it's quick and interesting - and the Gion Area of the city is very pretty especially at night. I also really liked Higashi-Hongan-ji. I thought it was really beautiful and peaceful. Hope this helps.