London is easily accessible. The historic dockyard in Portsmouth is half an hour away and has Nelsons HMS Victory and King Henry VIII Mary Rose.
Also within half an hours drive are Southampton, the ferries to France and the Isle of Wight which make good day trips. Both Southampton and Portsmouth offer excellent shopping/leisure opportunities including the outlet centre of Gunwharf Quays.

There are several beaches nearby including Southsea and Stokes Bay and a little further away is Bournemouth and Studland. There are great walks nearby including South Downs Way, New Forest National Parks (where ponies and cattle roam freely), coastal and country walks. There are excellent off road cycling tracks in the national parks (bike hire available) as well as on country lanes directly from my house. Fishbourne Roman Palace is less than an hour away and a great place to visit for any school children studying the Romans. Also, Intech - a 'hands on' interactive science and technology centre.