Brighton is always a good place to go, plenty to do there, although the Volks Railway is shut for the winter, and the aquarium is closed for renovation. There's plenty to see if you wander around the town and along the sea front, plenty of bars pubs and restaurants, and the pier is open all year as is the Royal Pavilion, which I will probably visit if the weather's not good. A plusbus ticket might be a good option also - see the remains of the Daddy Longlegs Railway at Ovingdean although there's only a line of concrete blocks to show where it ran. Or if you were feeling energetic and you do a bit of research you could trace the route of the branch to Devils Dyke (don't know if plusbus goes that far out though).
I had hoped top do a sewer tour but it looks like they only do them in the summer.