Ham House, directly across the Thames from Twickenham (accessible by a seasonal foot ferry from Orleans House, or a longer walk via Richmond Bridge), is one of the most remarkable Stuart mansions in England. Built in 1610 and expanded in the 1670s, it has one of the most intact 17th-century interiors in the country — dark oak panelling, original textiles, and furniture that has barely moved in 350 years. The National Trust manages the house and has done minimal restoration, preserving its authentically gloomy, intimate character.
The formal garden has been restored to its 17th-century layout, with parterres, a wilderness, and kitchen garden. It's worth combining with the Thames-side walk between Twickenham and Richmond — an afternoon that takes in Marble Hill, the river, the Ham ferry, and the house itself is a very good use of a day.