If it were me, I'd do:
- 4 nights Kansai, 4 nights Tokyo
or
- 1 night Nikko, 4 nights Kansai, 3 nights Tokyo (or flip Kansai / Tokyo nights)

When I say Kansai, I'm talking about either Kyoto or Osaka or even Kobe (specifically Shin Kobe). Changing hotels during vacation is a hassle. If Kyoto's your big highlight and you anticipate spending >/=2 full days Kyoto / 0-1 day Osaka, then you should stay in Kyoto. However, if you think you're going to do 1 day Kyoto / 1 day Hiroshima / 1 day Osaka, etc, then Osaka and Shin Kobe are worth considering. You'll likely get better bang for the buck hotel-wise, even in Osaka's Umeda area rather than Kyoto. Kyoto is just a short train ride away from Osaka (via Hankyu from Umeda or JR train from Osaka Sta... you could take a bullet train from Shin Osaka but no great hotel in Shin Osaka) or from Shin Kobe (via bullet train... there's a CrownePlaza right next to the station).

Everyone has different thoughts on how much time to spend in Kyoto, whether/not Osaka is worth it, etc. But that all depends on your interests, any hotel points/preferences, how much time you have on your trip. If I were planning a general trip for a friend visiting Jpn for the first time and there were 4 nights in the Kansai region, I'd probably recommend 2 full days in Kyoto and 1 full day for a day trip to Hiroshima & Miyajima.