Should I stay in Tokyo or Kyoto longer?

I have somewhat of a tentative itinerary written up for a trip I plan to take to Japan in May of 2010 (planning to avoid the Golden Week).

I anticipate my trip to be about 10 days, 9 nights. As it stands, I have three days in Tokyo, four days in Kyoto, and three days in Yakushima (which'll probably wind up being only one full day, since you have to worry about travelling from and back again to the mainland).

I put only three days for Tokyo because I feel like there is only a handful of things I'd like to see there, and a whole lot of things I'd like to see in Kyoto. However, prevailing opinion seems to suggest that Kyoto is worth no more than a three day stay. So should I switch it to four days in Tokyo and three in Kyoto? Can anyone provide any insight?

Additionally, what are the best places/districts/locations to stay in Tokyo, Kyoto, and Yakushima, so I know where I want my hotel to be?

Thanks!

However, prevailing opinion seems to suggest that Kyoto is worth no more than a three day stay.

I completely disagree. If you have the time and interest, Kyoto is worth seven days or more.

So should I switch it to four days in Tokyo and three in Kyoto?

It comes down to your personal preference. Both cities have enough attractions for at least seven days each. Tokyo is mainly about modern Japan and shopping, while Kyoto is mainly about temples, history and traditional culture.

Additionally, what are the best places/districts/locations to stay in Tokyo, Kyoto, and Yakushima, so I know where I want my hotel to be?

In Tokyo, I recommend a location close to a Yamanote Line station. I personally find the areas around Tokyo Station, Shinjuku Station and Shiodome most convenient and attractive.

In Kyoto, I personally prefer the downtown area (walking distance from Shijo Street and most of the good dining) or the Higashiyama district, although there is not much accommodation to be found there. I also like the Granvia Hotel inside JR Kyoto Station.

On Yakushima, it depends what you want to do. If you want to hike to the Jomonsugi, I recommend to stay in the Anbo area.

I'd definately stay longer in Kyoto. I recently spent 5 nights in Kyoto and there were still heaps of things I wanted to do in the region but had to leave. After two nights in Tokyo I was quite bored with it. There aren't many 'must see' sites in Tokyo in my opinion, whereas I probably could have spent a month in Kyoto seeing sights in the city and taking daytrips.

I completely agree with Uji. And, in addition, Kyoto is a great jumping off point for Nara, Fushimi, Uji, etc.