The garden's car park is no longer pay and display and has a tendency to fill up in the summer. You must get your parking permit from in side the visitor centre. There is a very small car park at the side of the road in Steephill which is £2/day and free roadside parking between Steephill and Ventnor. This does get busy at weekends though.
There are lots of pay and display car parks in Ventnor town and on the seafront. 'La Falaise' car park is just above the Spyglass Inn and its a lovely 20 minute walk along the coastal path to Steephill Cove and the Botanics.