This question is often asked by people on this forum, so I though I would provide a link to this topical article I just read entitled "London's best historical pubs". Of course there is no such thing as "the best pub" but this list does contain some of my FAVOURITE pubs in the center of London. I suggest having a read and then checking them out on Google Streetview as some are gorgeous to look at, like the Cross Keys or the Lamb. Choose a pub that Dickens, Elizabeth I or (gasp) Madonna have frequented.
I must add that for purely excellent Ale & Cider then you can visit "The Harp" (47 Chandos Pl, London WC2N 4HS) just off Trafalgar Square.
Cheers!
Steve.