My opinion, the best of the locations is Premier Inn Southwark at Borough Market:
http://www.premierinn.com/en/hotel/SOUANC/london-southwark-borough-market
Rooms from £64.00 each. On-site restaurant serving very good food. Walk to nearly every London tourist attraction. See photos, one room has a queen bed with a twin: http://www.booking.com/hotel/gb/premier-inn-london-southwark.html
Perhaps you could book two adjoining rooms, or two rooms next door to one another.
This hotel is near the River Thames for a beautiful walk along the riverbank. Walk west along the riverbank walkway to get to Westminster Bridge, Westminster Abbey, Houses of Parliament, Buckingham Palace. Walk north across the river to get to St. Paul's. Walk east along the river walk to get to Tower Bridge; walk across and you're at the Tower Of London. Located near your hotel: Shakespeare's Globe Theatre, and Tate Modern Art Museum. Borough Market is a market with food stalls selling all kinds of fruit, cheeses, pastries, and there are restaurants and cafes there. I have stayed at this hotel twice, and loved it.
City buses are good transportation, except they won't run on Christmas Day, of course. On other days, you can get almost anywhere in London by walking, city bus, or a combination of the two. Use your Oyster cards to travel on the city buses. Cheap and fun way to travel. The RV1 bus comes right by your hotel, and will take you to the London Eye in one direction (going west) and traveling east, to Tower Bridge, and Tower of London.
When you were asking about Marriotts, you mentioned several locations. Regents Park is the best of the locations that you mentioned. Regents Park is beautiful, and contains the London Zoo, which your children may enjoy. Transportation is good from there, also. I think this Marriott would work for you. Would also have a restaurant where you could eat meals Christmas Day. Could be a bargain, if you have some Marriott points to use up.
Do you have a good map of London? This would be useful to have right now for planning and choosing a location. And you will need one, of course, to find your way around London once you get there.
You will need to figure out where you will be eating Christmas day lunch or dinner. Many restaurants are closed then. That's why it can become important to stay at a hotel that has a restaurant on-premises which will serve you a meal on Christmas Day.