All the London haters out in force...
There's so much to do, I'd start with markets and you can keep on going back to them. Camden is pretty awesome, go to the stables market. Borough market obviously for food. From borough you've got the whole south bank so you've got tate modern, globe, national theatre, oxo, and lots more. It's also a great walk along the river (Go from shad thames to London eye).
At shad thames you have the design museum and some nice restaurants. Go over tower bridge and you have st katherines docks which is worth a quick wander round, then go to tower of london which is a good day out.
London bridge you've got borough market, go watch the shard being built too... Globe theatre is great and the swan bar there is nice and does good cocktails.
Further back from the river you've got southwark tube. Lots of nice bars there as well as the young and old vic theatres. young vic has a nice bar and does great burgers.
oxo tower has a nice restaurant at the top. Take your girlfriend up there and she will love you forever.
national theatre is a cool building to look round, always events going on in summertime, and look out for various food markets/installations around that area, as well as royal festival hall etc etc.
London eye is great, you get a fantastic view.
So... that's a river trip. It's also worth getting on one of the boats to greenwich. It's good to see london from the water and greenwich is a nice part to wander round, head up the hill to the royal observatory, there's a naval museum there too.
Visit the parks if the weathers nice, head out further on the overground if you can, hampton court palace is worth a visit, richmond park is nice for a walk and its full of deer.
Go watch some twenty20 cricket at lords after work.
Obviously all the free galleries/museums.
Head out to hoxton square, old street and many more places for nice bars.
Don't take the tube, get buses, you see where you are and quickly get your bearings. Londons not as big as everyone thinks it is, you can walk most places centrally.