They function 24 hours a day. The sea taxis -as the land taxis- can take you to any spot of the island from the harbour of Dapia.
But the best solution about the transportation in the city and in the whole island is to rent a bicycle: it is cheap, healthy, romantic and pleasant!
They can transfer the visitors at the most spots of the town of Spetses. You can "rent" them at the harbour of Dapia or at the Bouboulina square.