I often took the chance to have a swift jar at the Bishop's Mitre on Hatton Garden. Well, kind of on Hatton Garden (the nearest tube station is probably Chancery Lane on the Central Line), you look for a little alleyway with an easily missable sign on a lamp post, follow the alleyway and you get there. Much real ale goodness. Often used to meet friends in their function room - the room was upstairs and one of the friends was a wheelchair user but she loved the pub and didn't want to meet at another venue, so a few of us carried her up the stairs so she could join in.
Last time I visited London I must admit I really enjoyed just walking the streets and seeing the sights, even the really touristy ones. My wife and I walked along the Mall many times, walked through the West End and the City just to see the architecture and take in the buzz. I must admit I got rather tired of it when we lived there, but having the benefit of combining being tourists with knowing the back roads better than the masses meant we could see what we wanted without getting caught up in the crowds when we were ready to move on.
Years ago we had some friends from USAnia come to visit and we took them on a river cruise. I think we started at Westminster and got off at Hampton Court. There may have been an option to go a little further but we were pretty close to the edge of the world so feared falling off into space if we did, so we quit while we were ahead. Then of course from Hampton Court you can see the palace (pretty touristy), take a short walk into Bushey Park (not so touristy) and, if you're so inclined, walk through the park until it spits you out in Hampton Wick near Kingston Bridge. If you end up there, go the roundabout on the west side of the bridge, turn left and shortly after the electric bike shop is a little cafe called Hussars. I've always had good coffee there. Just don't ask for tea if you're easily offended. And, since this is a cycling forum, you'll be very close to Sigma Sport where you can spend sums of money with big scary numbers after the pound sign on very nice bicycles.
If you're really into walking you can walk along the Thames from Kingston to Kew Gardens and further. It's a bit of a trek but if the weather is nice it's nice and picturesque. When I lived in the area I often cycled that way.
