I'm a keen photographer, love ships and boats and I have a free pensioner's bus pass so I often go to Southampton, take a bus to Town Quay and then wander over to Mayflower Park if I see anything interesting. From Mayflower Park there's an excellent view of any ships which are in the berth next to it. Unfortunately, the park itself is tatty. There's a wooden shelter which looks much the worse for wear, a sports court which has seen better days and not much else. The kiddies' play area looks well stocked (from a distance anyway, as I have no kids of that age any more I haven't been in it) and the car park - although fairly small - is a reasonable size if you just want to spend an hour or so there. On the plus side there's always a lot to see if you like the sea and ships and there's a good view over Southampton Water. On the minus side it could do with an overhaul: nothing major, just a bit of sprucing up.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.