Kyoto can also be cold - but I'd suggest Kyoto rather than Nikko.

For Dec. 25, I'd suggest the Granvia. Staying at the station allows you to drop your bags and go straight out. And next morning you can leave bags with the concierge - ready to pick before catching the Shinkansen back to Tokyo.

Assuming you arrive in Kyoto around 2.30pm, you'll probably have time to see one thing before dark. You could make it to the Nijo castle, for example. Last admission is at 4pm and it's closed from Dec 26 through Jan 4, so that day is your only chance to see that particular place.

For the next day, you should pick an area to explore in depth. Best to check very carefully that the places you might want to visit will be open. If you want to cram the max into one day, you could get a very early start at the Kiyomizu dera.

For Dec 26, I'd suggest staying at a hotel near Tokyo Station. Either the Hotel Metropolitan Marunouchi or the Marunouchi Hotel (there are also cheaper business hotel options towards Nihonbashi).

Staying at one of those places makes it quite comfortable to use the last Shinkansen from Kyoto to Tokyo. That means you can enjoy dinner in Kyoto, catch the last train at around 9.30pm and arrive at Tokyo Station shortly before midnight. It's not bad when your bed is just a couple of minutes walk away.

And in the morning of Dec 27, you can easily catch the 7.30am or 8.00am N'EX to the airport.