If you're in the vicinity of Hampton Court, you'll be able to take a stroll around some of the palace's grounds for free, but will need to buy a ticket if you want to enter its buildings. The price of a ticket includes access to the palace, maze and formal gardens. Your entrance fee will also entitle you to a recorded multi-language audio guide, children's activity trails and costumed guided tours. You can buy entry tickets online, over the phone or in person at the palace's ticket office. National Rail (nationalrail.co.uk) regularly runs a promotion that entitles holders of valid train tickets to 2-for-1 entry to the palace, so traveling to Hampton Court by rail could save you money.
Paying for a tour of the palace may be a bit pricey if you're traveling as part of a large group. If this is the case, you can buy cheaper tickets that will entitle you to use the palace's maze and entry to its formal gardens, English weather permitting. The palace's gardens consist of 60 acres of land and include fountains and over 200,000 flowering bulbs. The Privy Garden, which runs from the palace down to the banks of the Thames, has been restored to appear as it would have in 1702, during the reign of William III. The Hampton Court maze was described in 1926 by English historian and barrister Ernest Law as "the most famous maze in the history of the world, and immeasurably the one most visited."
Immediately over the road from Hampton Court Gate to the north of the palace is Bushy Park (royalparks.org.uk). The royal park is free to enter all year round and open 24 hours a day. It's home to a number of plantations, grasslands and water gardens as well as herds of red and fallow deer, which roam freely, much as they did when Henry VIII hunted there. Bushy Park is the second largest of greater London's eight royal parks.
From around the beginning of April until the end of September, Turks (turks.co.uk) and Thames River Boats (wpsa.co.uk) run ferries from the bank of the Thames outside Hampton Court Palace to Kingston, Richmond, Kew and Westminster. A trip into the center of London takes over two hours. If you fancy stretching your legs, consider a walk along the river's banks to Kingston where you'll be able to grab a bite to eat at one of the town's riverside restaurants or pubs.