If you like quirky London and/or shopping
✵ Visit Eel Pie Island: Normally this private island on the Thames refuses visitors. But twice a year (in the summer and in the run-up to Christmas) they open up the footbridge from Twickenham and let the public inside. In particular you're invited to the island's boatyard, a proper working boatyard no less, and the two dozen artists' studios beyond. Here you'll find the artists themselves hoping to sell you some of their wares, including mosaics, ceramics, pottery and some caricature Christmas cards, plus some warming drinks in case you're very cold. It's a fascinating place to visit, at least once in your life, and you might get some presents bought too. [Saturday and Sunday, 10.30am-6.30pm]
If you like space
✵ Look inside the European Space Expo: A geodesic dome has popped up on Horseguards Parade, temporarily, housing an exhibition about the European Space Programme. There are 12 touchscreens to explore, covering all aspects of supra-atmospheric scientific endeavour. But don't think astronauts and space travel, because that's all old school. Instead the ESA does a lot with satellites, specifically networks of satellites looking down upon us. They've developed a system called Galileo, and a satnav system called EGNOS, which'll offer far more accurate positioning than your bogstandard GPS. It'll allow surveyors to pinpoint boundaries better, and geocachers to find hidden treasure quicker, and farmers to herd cattle using virtual electric fencing. If you thought space was exciting, think again - today it's primed to support job creation and economic growth. There's not much at the expo a website couldn't deliver, but it beats fighting the crowds on Oxford Street. [Saturday and Sunday, 10am-6pm, free]
If you're in southeast London
✵ Catch an old bus in Bromley: The single decker RF bus is 60 years old this year, and there have been several special services and anniversary road runs to celebrate. This Sunday it's the turn of the 227 from Chislehurst to Crystal Palace, plus a variety of other routes in and around Bromley. If you're in Orpington, Petts Wood, Shirley, Coney Hall, Eltham, Grove Park or thereabouts watch out for the vintage vehicles from about 10.30 onwards. [Sunday, free]
If you can't keep away from trains
✵ Go watch some steam trains: Ian has the details. [Saturday]
✵ Hunt down the new tube map: They're out there, I've got one. And they're on the TfL website, now with added Overground South. Given that no new stations or line extensions are due over the next three years, this could be the last new tube map until 2016.
✵ Ride a new train to Barking: The Metropolitan line's already got its new S-Stock trains, and now they're being rolled out on the Hammersmith and City line too. So far the shiny 7-car trains have taken passengers no further east than Moorgate, but this Sunday one nudges out to Barking and back, three times. The timetable, if you're interested, is HMS 0706/BKG 0807, BKG 0815/HMS 0914, HMS 0925/BKG 1027, BKG 1035/HMS 1134, HMS 1146/BKG 1247, BKG 1255/HMS 1354 (then to depot).