Hampton Court Palace is one of my favourite royal palaces, located on the banks of the River Thames in the Borough of Richmond, it is one of the most visited historic sites , with approximately half a million visitors per year.
Hampton court is located 40 minutes outside of London easily accessible by a direct train from London Waterloo, and due to its West London location could also be easily visited on a Heathrow stopover though I would suggest catching a cab which takes about 20/40 mins depending on the time of day and costs approx £30 each way. It is possible to get there on public transport but I would allow at least 90 mins each way.
Hampton Court was originally built for Cardinal Thomas Wolsey, a favourite subject of King Henry VIII, as Wolsey fell from favour, the palace was passed to the King, who enlarged it.
As well as the main house there are lavish gardens of over 60 acres that feature fountains, and displays of over 200,000 flowering bulbs as well as the world famous maze, its one of the oldest surviving hedge maze in the UK, which includes half a mile of pathways.
Its easy to spend as little as a couple of hours to a whole day here, there are cafés on site, frequent family activity days as well as concerts in the grounds and the Hampton Court Flower Show held once a year in July. For opening times and entrance fees check out the official Royal Palaces website here http://m.hrp.org.uk
If your feeling adventurous and fancy seeing more the the waterway you catch the river boat back into Westminster Pier which is located by Big Ben, it takes a leisurely 3 hours each way. Find out more info here http://wpsa.co.uk