I have a suggestion on the "how to get there" portion of the trip more than the "what to do there" portion.

Go to http://www.ba.com (British Airways) and register for their "specials" email. By doing so, my wife and I were able to find $200 round trip flights to Heathrow (and then we took the train to Glasgow) and saved a buttload of money that way.

BA runs specials like this a lot, it seems. Plus, if you're like us, you'll walk off the plane just as the paparazzi are arriving at the airport to see the contestants from the British version of I'm a Celebrity - Get Me Out Of Here! arrive, and you'll walk into the main terminal to the crowd clamoring to get your picture.