In The Empire Strikes Back, why is Yoda living on that lonely, remote planet?

There are parts of Dagobah that are "strong with the Dark Side."

After Emperor Palpatine came into power and there was a purge of the Jedi, the few Jedi remaning alive hid, hoping to be able to do something more in the future.

Because Yoda was a powerful Jedi, he hid near a source of darkness that would hide his presence so any Sith looking for him would not be able to sense his presence easily.

(Much of this comes out in Revenge of the Sith.)