Once you are in central London lots of it is walkable.
I would plan your days well coming into Victoria each day and then looking to get a bus to a point where you can walk for the rest of the day and then bus back to Vic.
Look at at the attractions/sights you want to do and then group them into 3 areas.
From Victoria itself you can easily walk to buck palace, through green park, Piccadilly Circus, Leicester sq, Covent Garden back down through Westminster, seeing Big Ben/houses of P, Downing Street and back to Victoria. Spread it out over the day stopping in between.
Another day train to vic walk to Hyde Park Corner, Knightsbridge (Harrods) Kensington palace gardens - Diana statue, park and fountain, plus museums like V&A, natural history, Science.
Then another day you could do train to st Pancras (do kings x and Harry Potter trolley) then walk past British museum, Oxford st, China town, Regent's Park.
So many possibilities - just decide what you want to see!