7 nights Tokyo & Kyoto with side trips in mid-December

Hi,
None of the places you mention offer any skiing. If you want to ski, I suggest you take a day off of Hakone and go to Gala Yuzawa for a night. You can use your JR Pass to get there and it is relatively close.

For Hakone, I suggest you get a Hakone Free Pass to see the area. The Loop Course is a good way to see the sights - you can cover them in a full day with an early morning start.

If you do all the above on a JR Pass, you can get some good savings.

Seven days is not much time - there are many very good day trips you can take on both ends, but beyond the above you simply don't have time. That said, I suggest you take half a day from Kyoto and go see Nara either. In Nara, the Todaiji Great Buddha is an extraordinary place, not to mention Kasuga Shrine, Kofukuji Temple, the Isuien Garden, and feeding the many deer in the area.

For Kyoto, try to time your visits to places to be more effective. The Fushimi Inari Shrine is open 24/7, so fitting it in early in the morning or evening allows you to add other places in between, and you can avoid a lot of the crowds at either time. The Honganji Temples open at the crack of dawn and are within walking distance of Kyoto Stn. so they are easy to fit in too.

Honestly, I'd normally say that for just 7 days, it would be better to just stay in the Tokyo area and see the local sights. But if you are not thinking of returning to Japan in the foreseeable future, you just have to do the best you can with what you have.

Good luck.