It's the witout a car that's the difficult bit.
Catch a 31 bus to Dunstable, walk out and see us at the London Gliding Club. We may be able to take you flying depnding on how busy we are (for a fee of course).
www.londonglidingclub.co.uk Get a taxi either from the airport or Dunstable and go and see Buster at Whipsnade
Get the Virigin Bus from the terminal to Milton Keynes and go skiing at Xscape, go shopping (if you must) or just walk in the Parkland; Willen Lake for example. You could go to the theatre cinema etc. (see MK web; type it into Google)
That's a start.