the place to head for, with free parking is the John Bradfield Viewing Area which is adjacent to Landguard Fort & can be found here: https://goo.gl/maps/HfDyycFay5L2
The Viewpoint cafe is at the same location.
Take a deckchair & a book- it might even be sunny
Felixstowe faces South and photography is better in the (early) morning or evening.
Felixstowe / Harwich harbour can often have quiet periods, at other times there can be a few simultaneous movements.
Harwich Harbour Authority's website showing some departures (including Felixstowe, Harwich, Ipswich) can be found here: http://apps.hha.co.uk/mis/traffic/Departures.aspx
The times listed on the Port of Felixstowe's expected arrivals page indicate times alongside.
Big ships, especially those which require to be turned 180 degrees before berthing, can be rounding Landguard Point (which is within view of the Viewpoint) 45 to 60 minutes before the indicated times of berthing.
The nearby Felixstowe seafront, i.e. Sea Road (a 2 minute drive from the viewpoint), also offers wide views of the North Sea and approaching & departing vessels, but is not really suitable for photography.
Ditto here: https://goo.gl/maps/ucDWkk9NeNs