Other than your choice of places to see, I find almost nothing about your plan to like.

I'd recommend activating the 7-day Rail Pass immediately upon arrival so it will cover the trips NRT-Shinagawa (Tokyo) on the Narita Express and Shinagawa to Osaka on the shinkansen. That is likely to be your most expensive travel day and it makes no sense to pay it out of pocket. Additionally, the Rail Pass will be little use to you after you arrive back in Tokyo. Activating for 10-4 through 10-10 covers all of your most expensive travel.

Unless you want to change hotels a lot, there is little point in changing between Kyoto and Osaka. The cities are only a few minutes apart by shinkansen and not much longer by local train. The best recommendation is to pick one or the other and day trip between them. Nara and Himeji are equally easy to reach from Kyoto or Osaka - perhaps even easier from Kyoto. I prefer Kyoto as a transportation hub as the main station is right downtown where Osaka requires a short trip out to Shin-Osaka to use the shinkansen. Others prefer to stay in Osaka because the night-life is better.

Likewise, why are you moving hotel during your Tokyo stay? That just wastes time you could be seeing the city.

Suggest you get a prepaid Suica card in Tokyo to use subways and local trains to get around. The Rail Pass won't cover those.

You have allowed only 3-1/2 days for Kyoto, Osaka, Himeji and Nara. That really doesn't give you time for any of them. I'd suggest staying in Kyoto and taking 2 days there as well as a day for EITHER Osaka + Nara or Osaka + Himeji. That last 1/2 day could be back in Kyoto, doing the things and places you missed, prior to catching a mid-day shinkansen to Tokyo.