If you are over 60 you can get a 'concession' Oyster card which will save you money (must check up on mine!). The trend though by TfL is to go contactless, i.e. use your bank debit card, providing it has the 'contactless logo' on it. The same software that caps daily Oyster card charges, does the same for your card. My wife has ditched her Oyster card and just uses her debit card now, and one could suppose that in years to come Oyster card usage will be much reduced if not actively discouraged. For the time being though, they are in my booklet, A Good Thing!
Remember when planning excursions that the weather can be cold, windy and wet, or alternatively bright and clear and cold, and/or all variations and combinations in between, possibly in the course of a single day, so dress accordingly! It will certainly get dark early too, around 4.30 pm, so if wanting to view the sights early is better than late (it will get properly light by around 8.00 am).
I echo the suggestion of checking out London Walks, lots to choose from so something in there for all interests you'd think but I would definitely check out the opening hours of the main attractions. Some properties, i.e. National Trust, close October through until March as a general rule. I'm pretty sure that the Historic Palaces of London are all open, but may be operating on a scaled back opening schedule (perhaps a London dweller on here can advise, but the websites for each attraction will tell you).
We enjoyed a couple of things when visiting London early in the year. Try go and see Westminster Abbey on it's late opening evening (Wednesdays?) - much less crowded and wonderfully atmospheric in the dark and the docents have more time to chat to you too. The crypt restaurant there is good too, economically priced and decent food, worthy of investigation.
We also booked tickets for the Sam Wanamaker Theatre which is open through the winter and attached to Shakespeare's Globe on the south bank - it is lit by candles for the performances and again wonderfully atmospheric. It is tiny too, seating only a couple of hundred so don't leave it to the last minute to book. We went to see a play called, if I recall, something like 'All The Angels' which was about the writing of Handel's 'Messiah' and it was fantastic. A play about a German composer in a reproduction of a Jacobean theatre, built by the efforts largely, of an American. And with a pub attached (the Rose) - what could be better! The Globe website will tell you what's on while you are there - the main Globe theatre is closed until March, it being open to the elements, but there are productions on at the Wanamaker throughout the winter. We took a gamble on the play we went to see and it rewarded us magnificently!
It may be a bit late for your trip, but it is also worth trying to get tickets (they have to be advance purchased) for the the Ceremony of the Keys which is the official locking up of the Tower of London on a nightly basis. The Beefeaters politely (but firmly!) turf you out at the end! It's not a long ceremony, but an ancient curiosity and the dark adds another dimension to it all, the Tower and environs being dimly lit as you might expect.
Hope you have a fantastic trip!
Ian