When I stayed in London after a Princess cruise, I bought a Princess transfer to the Victoria bus station and took a cab to The Rembrandt. Reasonably priced, nice breakfast and near Harrods. The Victoria and Albert Museum was across the street. I don’t remember the nearest metro, sorry. But the hop on bus had a stop at museum. Very quiet neighborhood but a trek to the Thames and landmarks there.
the bus station can be quite hectic and is large, so depending on your age and luggage, it can be difficult but doable. It seems all the transfer buses arrive at once and it can take a bit to sort out.
Good luck!