Mile End Park in East London, White grounds near the Thames, and of course South Bank. All really fun spots. Then for shops Slam City in central London, and Parlour which is next to Mile End.
Shoreditch is an awesome area, lot of cool stuff to do around there and fun bars to check out. Brick Lane is close by and is a cool spot too.
If you just skate around though you'll find plenty of spots in Central London, but that'll get you started.