What should I do in London, UK?

I’ll be going to London for a weekend. I’ve never been before, but only have 2 nights and one full day there. I can’t stay any longer. So, what should I do? Where should I go? I’ll be staying with friends, so they’ll show me around, but is there anything pressing that I should really experience? Please keep in mind, I’m not into total touristy stuff. I like pubs, I like comedy, I like art… Is there any kind of underground theatre scene or really cool nightlife that anyone knows of?