You mentioned Portsmouth. Best spot for view and photographs at Portsmouth is the Round Tower. Take the train to Portsmouth Harbour Station, then follow the millennium trail south for about twenty minutes on foot. There is a tourist information centre at the Hard Interchange, just outside the station, with excellent free maps.
If you are in this area, another good option is a round trip on the Red Funnel ferry from Southampton to Cowes on the Isle Of Wight. From Southampton Railway Station take a bus to the ferry terminal at Town Quay (I think it's free). The ferry passes close to vessels at the Eastern Docks, and Fawley, and Hamble if any alongside, plus anything on the move in Southampton Water. Round trip takes about 2-1/2 hours.