I love swimming and I love being outside. London is great if your into both these things. I swim at London Fields Lido which is heated all year round. Its best in the winter when the steam rises from the water and if your lucky its snowing a little on your head. If your brave you can also go for the unheated option of the Serpentine or Hampstead Ponds.
Getting lost is an age old suggestion but a good one. Put away your cell phone or your A-Z and just wander around. I still do this regularly even though Ive lived here for nearly 10 years. London is a big city and it drip feeds you its secrets sometimes. You will come across things you wouldn't usually, in amongst the Starbucks and pret a mange there are some amazing sights. Just 'being' somewhere is a great experience and one no guide book can help you find.