My hometown is Hastings, so I'm a little biased towards it as one of my favourite seaside termini - a lot of services do terminate there, so I'm counting it as a terminus.
The cutting on one side together with semaphores and working signal box give the station a more bucolic feel than most other seaside resorts, and stepping out of the station to see the castle ruins up on the cliffs and the 'Welcome to Hastings' message daubed on the side of the Seadog pub always reminds me why I love the town. Obviously, the new station building isn't as grandiose as the much-missed Southern Railway structure, but it's certainly not soulless with its yellow stone and blue glass. From a more practical perspective, the bus stands are right outside and it's a short walk to the town centre and beach. Pity about the derelict eyesore that is Queensbury House, but word is the owners are actually starting the long journey to convert it into flats.
Oh, and I do love how each line has its own character. A slow jaunt through the wetlands of Kent on the Marshlink, snaking through the laborious High Weald terrain to Tunbridge Wells, or enjoying the sea views and a quick glance at the St Leonards depot on the East Coastway.
Brighton was mentioned before, and the view from the London Road Viaduct is as amazing on the hundredth journey as it was on the first. It really feels like a proper terminus too, a little Victoria as someone called it on this thread.