You can drive to Abney Hall and you can park for free after 1.30pm on a Saturday or on a metre before 1.30. It's free all day on a Sunday.
You can get the train to Stoke Newington overground train station and Abney Hall is about a 15 minute walk but you can walk through Abney Park Cemetery which is just amazing!
You can get the 73, 476 or the 393 to Stoke Newington Church Street and the bus stops nearly outside Abney Hall. You can't go wrong.