The District line is the best of the Tube options, stopping at Turnham Green (in the heart of Chiswick but a walk from the houses), Gunnersbury (for Syon Park), Kew Gardens, and Richmond. For Hampton Court, overland train is quickest: South West trains run from Waterloo twice an hour, with roughly half requiring a change at Surbiton. There are also regular, direct trains from Waterloo to Chiswick station (best for Chiswick House), Kew Bridge, Richmond (for Ham House), and St. Margaret's (best for Marble Hill House). London overground trains also stop at Gunnersbury, Kew Gardens, and Richmond.
A pleasant way to go is by river. Boats depart from Westminster Pier, by Big Ben, for Kew (1½ hours), Richmond (2 hours), and Hampton Court (3 hours). The trip is worth taking if you make it an integral part of your day, and know that it gets breezy. Round trip costs between £18 and £23. For more details contact Transport For London (0843/222–1234 www.tfl.gov.uk).