I faced the same dillema a year ago! I would suggest going on the London eye, seeing Big Ben and parliment, possibly seeing the changing of the guards, shopping somewhere like Harrods or in Piccadilly Circus, and take the underground or a double decker bus to get there! Stroll through parks, and relax! Try to be sure to dine in a true pub if possible! London is the best!

If you are interested in stonehenge, you should see it or rather go to Avebury, where you can touch the rocks and walk through them!

Day trips outside of London

Oxford/Cambridge/Hampton Court/Stonehenge/Windsor Castle

See the london eye, big ben, downing street, houses of parliament

Go on the tube

Get on a red bus

Open top bus tour, British Museum, National Gallery.

i would take the train to dover or canterbury