Kyoto: Get up early to see the temples when they are quieter, although because it is winter it should be reasonably quiet anyway. Realise you won’t see all of the temples, but also that each of the sites are very different so have a bit of a read up before you go, to prioritise. Don’t feel like you have to pay to get in everywhere, but do pay to go into a few of the temples and shrines to get a real feel for the place. I particularly liked the complex with Daitokuji in it and Kurodani. Although the geisha districts are now largely touristy, they are still nice to walk around in the evening and if you head out early (say 4-5pm) you will probably see geisha or at least geiko.
I think they are still renovating Himeji which is a shame.
For a romantic stay, ask your brother if there are any hot springs in the Osaka-Kyoto area. We went further north (where the monkeys sit in the natural hot springs near Nagano) and really enjoyed the natural spring baths (nice and romantic if you can find a spa hotel where you can book a private bath).
And if you are Tokyo with friends, you have to do karaoke.
Edit: And try to take the Shinkansen during daylight when you go to/from Tokyo to see Mt Fuji.
