If you’ve got a bike, get the train from Waterloo to Surbiton, head for the river and ride from there into central London or to Weybridge if you want a shorter ride (or a walk but if you do, start from Kingston). It’ll take you a bit, you can stop and get a beer and some food on the way. I gather there’s a couple of us STW people around that stretch of the Thames so you might be able to get beer buddies.
Get the tube to some place towards the edge of zone 1 like Earls Court and walk back to central London, stop in odd pubs and chat to people (or read if you’re that way inclined). I’ve had some good days that way surprisingly enough and you see more places and interesting stuff.
If you go to the Brick Lane area for the bike shops, go to Beigel Bake and get a salt beef beigel (beware of some of the dodgy curry houses down there though, there’s some absolute crap). While you’re over there, there’s good vietnamese up Shoreditch way too.