A couple of thoughts on Kyoto from me - I really enjoyed it, probably more so than Tokyo (although I did enjoy there too). There was more of a sense of history in Kyoto for me.

Given you get in to KIX in the morning, provided you can caffeinate yourself, you could use that time to see a few more things. There are a couple of things I really enjoyed in Kyoto - Kinkaku-ji was probably the prettiest place I went to - really lovely setting, although you can't go inside. I would imagine it would be stunning with snow on the ground. I found the Imperial Palace tour (you have to book this in advance, limited number of places each day) fascinating, really gave me a sense of how the place used to be. You could probably do a couple of the other things on your list that day as well if you want to make the most of your time. Be aware that several things shut quite early - 4, 4:30 pm seemed the norm for several places.

Slightly further afield, Nara was probably my favourite place I visited in Japan (it's a tough call, as everywhere was pretty amazing!) The Tōdai-ji is wonderful - you just can't understand the size from pictures. It's in a lovely park, with cute but cheeky deer everywhere! Kofuku-ji has a very impressive pagoda. It's an easy trip by train from Kyoto, and on the way back stopped at Fushimi Inari-taisha which I thought was very pretty, although I didn't stay there terribly long (walked one of the shorter routes and took a few photos then hopped back on the train)

I think you can absolutely spend a full day in Kyoto / Nara and then take the train in the evening, it is only about 2.5 hours to Tokyo. Hyperdia.com will give you train times so you can plan. Much easier than flying too!