Portsmouth

Portchester Castle
(http://www.english-herita...) - About 5 miles from Portsmouth is one of the best preserved Roman fortifications in Northern Europe. The castle's keep was built in Norman times largely from recycled Roman brick and extensive late Roman structures remain although ruinous. The original church is still in use and is popular in summer for weddings. The castle is well sign posted, and served by regular buses, Portchester rail station is only a 10 min walk north. The Cormorant Pub on picturesque Castle Street is a nice place to have a drink in a Traditional English pub.
Portsdown Hill
offers amazing views across Portsmouth and the South Downs. Just to the rear north of Portsmouth, it is a world away with countryside walks and traditional pubs.
The Royal Armouries at Fort Nelson
sits just on Portsdown Hill and is free of charge to visit.

Gosport shares the harbour with Portsmouth and can be reached by a short ferry ride from by Portsmouth Harbour station. Home of Explosion, Museum of Naval Firepower and the Royal Naval Submarine Museum.

Winchester, the former English capital is a beautiful city worth a visit. Excellent restaurants, interesting shops and of course the famous cathedral.

Chichester housing a lovely city centre and impressive cathedral

Emsworth this small fishing town is a nice retreat year round, but the food festival in the first week of September is a real treat, not to be missed if you are in the area.

New Forest just the other side of Southampton is one of the nicest rural getaways in England.

There are some shops in Southampton apparently, if that's important.