The National Trust
These include Petworth House, Nymans Gardens, Wakehurst Place, Standen and Uppark.
The National Trust also owns some of the very best outdoor places in the county too. Cissbury Ring, the Devil's Dyke and Saddlescombe Farm, the Slindon Estate, Drovers Estate near Singleton, East Head Beach, Harting Down, Bosham Quay Meadow, Black Down, Bramber Castle and Highdown Hill all come under its aegis.
The National Trust operates one huge website that contains the specific contact details and opening times for each of these attractions - these change, especially from season to season, so it's worth checking these with the National Trust before you go.
You can also book places for special events from their website.