Newhaven has a Ferry service to Dieppe.
Brighton to the West and Eastbourne to the, erm, East is a simple bus £4.00/2.00 taking about an hour and a half /half an hour or bus to seaford and train £3.60 return taking about half an hour by car it is easily accessible along the coast road.
South Downs Way passes thought the park, from there one could walk to Eastbourne or all the way to Petersfield in Hampshire
Go cycling in Friston Forest
Walk/drive/cycle up the valley to Alfriston