Hi,
Solely on the basis of hot spring experiences, I'd say Kinosaki is better. But in overall variety of things to see and do, Hakone is a better use of your time. Getting to Kinosaki is also extremely time consuming. Your next question is a bit unclear - make it to Kyoto in time for what? Seeing Hakone well takes up a full day. If you can do the traveling at night, then so much the better to maximize your sightseeing time.
I think your itinerary and my previous suggestions covers a lot of ground. The only other suggestions I can think of are, first for Himeji, be sure to see the castle but don't miss the Kokoen gardens next to it - they are very beautiful. For Nara, concentrate on seeing the Nara Park area - the Todaiji temple is a must, plus feed the deer around it and see Kasuga Shrine as well as Kofukuji Temple. Also don't miss the Isuien and Yoshikien Gardens - they are normally ignored by the tourist stampedes so they are quiet and beautiful.
For Tokyo, it depends on your interests of course. Virtually everyone goes to see Sensoji though, plus the Tsukiji FIsh Market is amazing to see organized chaos at its finest - but you'd need to be there about 4:30 AM to get in line for the tour. If in Tokyo on a Sunday afternoon, be sure to see Harajuku for the youth and the wild fashions, as well as Meiji Shrine and Yoyogi Park next door. The Tokyo Sky Tree is also pricey but offers a killer view over the city - twilight is best to see the city change from day to night.
For other ideas, see:
http://www.gotokyo.org/en/index.html
http://www.jnto.go.jp/eng/location/regional/tokyo/index.html
http://www.ar.jal.com/world/en/guidetojapan/city_information/tyo/see/akasaka/
http://www.japan-guide.com/e/e2164.html
Good luck.