Hi Gordon
Chas has covered most but you can also get good shots of Southampton traffic (not Esso tankers however) from Hythe Pier. Here you can take a train ride to the end of the pier, and also catch a ferry across to Southampton affording good views of vessels on berths 39 - 41 (usually car carriers or cruise ships) and also views into Ocean Dock. If you visit in the summer, Town Quay and Mayflower Park in Southampton give good opportunities for vessels arriving at the Western Docks (berths 101 - 110), No.7 drydock, and the container berths, but only before about 10am when the sun moves around. You should also note that Southampton arrivals are mostly pre 9am and most sailings after 4pm. Large container ships and crude tankers tend to come in on the high tide, which is double at Southampton due to the Isle of Wight effect. Large container ships often pass off Fawley as it is one of the few places where there is sufficient deep water width to allow a pass. So if you see a large box boat departure for say 12:00 and an arrival for 15:00, they will pass off Fawley.
hope this helps, enjoy your visit
Allan
oh and Chas, 0/10 for spelling