What to recommend, rather depends on what you like doing and how much time you want to spend driving rather than doing it. Goodwood is not too far from Brighton (Royal Pavilion) and Portsmouth (Victory, Warrior, Mary Rose). On the way to Malvern you could do Salisbury Cathedral, Bath and the Cotswolds. Once you are at Malvern you are within striking distance of the spectacular castles of North wales, although Ludlow is much closer if you wand a good castle. North of Goodwood just inside the M25 is Brooklands. Really, pick any part of the UK and you will find places of interest/natural beauty not too far away.
