Twickenham is well connected to central London by South Western Railway from London Waterloo — the journey takes about 30 minutes. Richmond is a 15-minute walk or two stops by train, and from Richmond you can access the District Line to central London.
For the Thames-side historic houses, walking is the best approach. A riverside walk from Twickenham Embankment to Richmond via Marble Hill and Orleans House takes about 45 minutes. The seasonal Ham Ferry crosses to Ham House from near Orleans House. Strawberry Hill is about 20 minutes' walk west from the town centre. Most of the notable sights are within easy walking range of Twickenham station.
On Six Nations match days, train capacity is overwhelmed — trains run packed from Waterloo and the walk from the station to the stadium fills the surrounding streets. Allow extra time.