Out of the hotels I suggested I would say that the Sofitel is the better situated. A few minutes walk to Trafalgar Square and Piccadilly Circus and around the corner from a few theatre’s.
Not sure if it has or will be open by the time of your trip but of course there is afternoon tea at the Savoy, within walking distance or short bus ride and of course the Ritz, which ever takes your fancy. You used to be able to book these on line in advance
Hope that gives you a couple of options