Are you in London for Christmas and New Year? There isn't much of a Christmas vibe in London compared with other countries. Visit the South Bank for the Christmas markets and the Wonderland at Marble Arch, which can get hideously busy at night. There are sometimes carols sung in Trafalgar Sq before Christmas in the evening, but these will not be announced until nearer the time. If you are not in London until after Christmas, I am not sure which of these will still be open.
The main shopping streets will have Christmas lights. Regent St has for the last few years had dreadful lights sponsored by that well-known British company Disney, which will be advertising their latest film. Oxford St is usually OK and Carnaby St is much better. Look in Burlington Arcade - their lights are good.
We use £ here not $ for pricing hotels. All central areas are safe and as the attractions are widely spaced, it doesn't matter where you stay, as you will always be close to some attractions and further from others. Accommodation over Christmas and New Year will be more expensive and there are transport and shop closures over the Bank Holidays. The weather should be OK as London gets little snow.
