Evict the widow

Evict the widow is an unmarked quest in Fallout 2.

Detailed walkthrough
The widow is in the small shack with the brahmin pen just southwest of the sheriff's office. If you go talk to her about her plight you can either kick her out like the sheriff told you or you can pay the $120 of back rent she owes. If you pay the back rent you receive 1500 XP as your reward. You also get paid $100 by the sheriff for completing the task so the net cost is only $20.