Depends on the weather I would suggest the usual Tourist sites, what are your interests ?
Oyster card will be best for public transport, or you could use a contactless cards. London Buses no longer take cash so you will need one or the other.
My wife and I visit London for a week every January.
Each day we see a west end theatre and use the 'Get Into London Theatre' promotion:
Pick up tickets at the venue box office and there is NO fee, just the ticket price of £10, £20, £30 or £40.
Most stores have January sales.
For events you can use sites such as 'Time Out":
and 'All in London"--'What's On":