There is a cutscene that indicates that the whale/ghost noise that constantly plays is coming from the sewer, and in order to enter I need to get the key from the museum curator. However, when I go to visit him, nothing happens.
So how do I get the keys? Do I need to get a certain number of artifacts? Is it a random reward?
According to the Stardew Valley Wiki:
The Sewers are unlocked by obtaining the Rusty Key after donating 60 Artifacts to the Museum. They can be entered either through the sewer cover in the South of Pelican Town or through the grates in the South of Cindersap Forest.
In the Sewers you can catch the Mutant Carp, which is one of the five legendary fish in the game.
Krobus is also located here and sells 'rare' items, including a Stardrop and Iridium Sprinklers.
