Daily events like Strange Brew are easy to do solo. Heart of the Enemy is one I do a lot because all you need is a scorchbeast DNA sample, and those things are all over the place.
Cop a Squatter is one of my favorites. You get this from the chief in Watoga. You are tasked with clearing a location of the enemies. But as long as you have this quest, it will complete even if another player kills them while you're in the same server. That happens a lot and the rewards are given even if you didn't lift a finger.
In that wiki link you see the list of Public Events. It isn't complete I don't think, but those are the ones that PM and I are on about..
To achieve anything in this game you must be prepared to dabble in the boundary of disaster — Stirling Moss
