Depends which country, at the moment I belong to two. In Scotland, go to Glasgow. Forget all that Edinburgh stuff and 'omg the hills and the walking'. Nah, go to the City of Glasgow and enjoy yourself. It's beautiful in its decay, the people are unbelievably friendly, and you can get a whiskey and coke for £1.85. I recommend Firewater, more expensive but the music's amazing. The subway is called the Clockwork Orange and is tourist-proof, and crazily cheap. Don't bother with an umbrella, it won't last five minutes against the wind. Plus the rain here is horizontal, so hoods are useless. Just enjoy getting wet.
In England, London. You want to go to Camden town, for your culture and your hipness and your weird clothes and cheap takeaway. Camden Roundhouse for gigs, beautiful. You also want to hit Trafalgar Sq because of the adjoining art galleries: it's not boring, it's amazing, give it a chance. There's a club near Leicester Sq called Zoo that does great cocktails, but I wouldn't bother if I weren't already in the area. Don't get confused by the tube, it's not that hard: get off before Brixton. Don't bother with all that houses of Parliament and Buckingham Palace crap, you'll just get your camera nicked.
If you're in the UK, these are six hours apart (by train), so choose wisely. Don't be fooled into getting recognisable snaps of red buses for your friends at home: choose life, choose Glasgae.