The old railway station has a web site:
http://www.old-station.co.uk/main.htm
On that site they have a small list of local things to do:
http://www.old-station.co.uk/main.htm
Nearby is Petworth House, a National trust property
http://www.nationaltrust.org.uk/main/w-vh/w-vi sits/w-findaplace/w-petworthhouse.htm
Nearby there is also the Weald and Downland Museum, where they rescue old medieval buildings and rebuild them on the site.
http://www.wealddown.co.uk/
If you have a car you are not far from the sea: Brighton, Chicester, Portsmouth, Worthing, Bognor.