Christmas/NYE London/Paris

This came up last month it might help you about what to expect
https://community.ricksteves.com/travel-forum/england/christmas-day-transport-from-heathrow-to-london-vauxhall

I've rung in the New Year twice 2015, 2016 in Paris and had a great time. Consider southern Spain also. We were in Cadiz last New Years day drinking wine at the beach watching the sun go down over the Atlantic it was 70 degrees and sunny and no tourists around. In Spain you eat a grape for each chime to midnight for good luck.

Erica,
i just spent Xmas and New Years in London and it was amazing. I would not split my time unless you have a full week in London and another week in Paris. London closes most everything on Xmas day including the underground and buses but I knew that because of this great blog. We rented a flat in Bloomsbury, across from the British Museum. All museums are closed for Xmas and Boxing Day but we had so much fun being with HUGE crowds on Boxing Day. The people in London were so very nice and festive and so much to do. Both cities would be great but cold and rainy of course but when you have Hamilton tickets, the world is great. But New Years Eve in London is glorious. I have spent many New Years there but don’t fly out on January 1st. I should have spent a few more days. I am planning my return to Great Britain now! Cheers, Kathy

I just spent Christmas in London from 12/22 - 12/27 and we had a GREAT time!
I was able to score tickets for the Christmas Eve Service of Lessons and Carols at Westminster Abbey which was wonderful.
We had Tea at the Wolseley, all decked out for Christmas.
We had Christmas Eve dinner at Maggie Jones's in Kensington. With a reservation there are many restaurants that serve Christmas Eve dinner.
Public transporation closes down around 11:30 PM Christmas Eve.
There are Christmas markets all around the city. We bought fixings for Christmas dinner at Borough Market - so much fun - and cooked Christmas Day dinner in our Airbnb apartment and opened presents. The owners even left their tree for us so it felt homey!
Christmas Day in London needs some forethought - almost EVERYTHING is closed except for a few liquor stores and ethnic restaurants. Literally ALL public transport is also closed so you have to plan ahead - cabs and Uber are available but at triple surge prices. We just went walking on Hampstead Heath that day which was close to our apartment - many other people had the same idea and it was great being out there with everyone and their cute dogs! There are restaurants that serve Christmas Day meals but you do need reservations because they book up well in advance.
The Boxing Day sales on the 26th were crazy but fun to experience. Public transport is open that day but on a more limited schedule.
We saw other things we wanted to do but didn't know about until we got there...didn't have time and/or couldn't get tix...
The Globe Theater does a wassail & carol event that looks fun.
The London Sky Garden has beautiful Christmas decorations where you can have a drink and enjoy views over the city.
There are performances of of A Christmas Carol at The Old Vic - tix sell out fast but we will try to get them for next year.
We were so happy with our Christmas in the city and might do it again sometime. They definitely know how to decorate for the season! Went up to Edinburgh for Hogmanay - New Years - and it was over-the-top amazing!!

London for Christmas and Edinburgh for New Year's Eve.

It's been mentioned in the replies already but for your planning on lodging and transport, I want to underline the fact that there is effectively no public transport available in London on Christmas Day. There is no service on any mode provided by Transport for London -- so no service on the underground (Tube), buses, TfL rail, Overground, DLR, trams and riverboats. Taxis are running but there is a £4 surcharge on black cabs.

As for the rest of the Christmas period, there is service but on some days (like Boxing Day, 26 Dec.) there are changes and reductions in service. Here's TfL's Christmas 2018 service advisories (sidebar on right for other days in the period) to get a sense of how it changes.

It's not an enormous deal, but is something to be aware of.

Thanks everyone for your helpful responses. I was thinking 5 days London and 5 days Paris excluding travel days. We would definitely not be flying in on Christmas Day but more likely a couple days before. My husband and I loved the festive atmosphere and simply walking the streets and seeing the lights which is why we thought it might be fun to spend the Christmas holiday there. I am still undecided as to how to divide my time between the two cities. How long do the Christmas lights stay up in London after Christmas? Would taking train from one city to the other eat up an entire day?
I also posted a similar question in the France section hoping for more Paris information.
Erica

The lights stay up through New Years in London. In fact, a friend of mine just posted pics from London yesterday and there were still some up where she was.
Going by train from London - Paris takes about 2.5 hours. Plus you have to manage the stations at both ends with checking in, passport control, etc. It will eat up a good 1/2 day at minimum. But get an early start or start later in the day and you won't lose too much time.