Can't believe you never flown before.
Places to visit...Clapham Common, Streatham Park or any random park after nightfall...opportunity knocks Marijan.
See all the sights. Tower of London etc. The Imperial War Museum is worth a visit.
Brixton.
Places to avoid...Emirates Stadium. (yes MJ I saw your post).
Don't carry a rucksac on the Tube...unless you want executing by the friendly London police.
Hackney.