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For clubbing in Tokyo, Roppongi, Shibuya and Shinjuku are your best bets. Not much budget accommodation in those areas though.

In Kyoto Higashiyama is good if you care about your hotel's surroundings. It can be a bit tricky (crowded buses that get stuck in traffic) to get away from it. Kyoto station area is very good for transport (trains, subways, bus terminal), but nothing fancy, i.e. just an ordinary Japanese cityscape. I believe generally there are more budget options around Kyoto station, so if all you do at your hotel/hostel is to sleep, I'd consider the Kyoto station area. You could always take an evening stroll in Higashiyama and return to your hotel at night.

perfect location in Osaka and Yokohama?
Depends a bit on your definition of "perfect". Unless you have a specific reason to stay in Yokohama, I would consider going there as daytrip from Tokyo (if you really have to go there). Also works well in combination with Kamakura, i.e daytrip from Tokyo to Kamakura (at daytime) and Yokohama (in the evening). On a trip of your length I'd spend at most one day in Yokohama.

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Thank you.

Would you recommend staying one night longer in Tokyo and only one night instead of two in Yokohama? Or maybe one more night in Osaka as my plan is to do a daytrip to each Nara and Kobe. Perhaps, 7 nights in Tokyo are too much, however, I don’t want to lose too much time by travelling around. But I assume that two nights in Yokohama are really too much.

Can you recommend a good hotel location for Osaka as well?

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I would not sleep in Yokohama at all as it is very close to Tokyo. Also with only 10 days in Japan, Yokohama would not be top priority for me (though I've been many times as I used to live nearby). Of course if you have a particular interest, go, but I believe for most tourists one day in Yokohama would be sufficient.

I don’t want to lose too much time by travelling around.
All the places in your itinerary don't take much time to get to. If you travel after dark (sunset is early in Japan), you don't lose much sightseeing time either.

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I will be in Japan for 15 days. ;)

However, I will reconsider the trip to Yokohama. I will probably go for one day and one night as I heard that the nightlife isn't that bad there. A possibility would be arriving in the early afternoon, exploring the city, enjoying the nightlife and spend the next day at Cosmo World before returning to Tokyo in the evening.

Thanks by the way for your suggestion of visiting Kamakura. I just read the Lonely Planet article and this sounds very nice.