From London you can easily visit some interisting places on day trips by train. It is for instance less than an hour by train to Winchester, if you want to see the Cathedral. New Forest, not far from Winchester, is another interesting place if you like nature and wild horses. Brighton is also only about an hour away from London. Brighton is among the favourite destinations for Londerners who want to spend a day out at the sea.
Closer to London are destinations like Oxford and Cambridge, world known for their universities, and Windsor and Windsor Castle. Other things to do on a day trip could be to sail on one of the Thames cruise boats that goes up the river or to visit LegoLand near Windsor.