There's a good mission called Tied Down that appears on my city map. When I get close to it, the good mission indicator appears on my minimap, but once I start getting closer, the mission disappears and I'm left with only the evil missions.
Once it disappears, it's gone from my city map, too. Once I complete another mission, it's back on the city map, but again it vanishes once I approach.
Am I doing something wrong? My karma is Champion rank.
You're doing nothing wrong. Probably, the quest is given by a cop, and they fight every enemy they see. While they are fighting, they can't give any quests.
Kill all the enemies in the area and check again. if that doesn't work, maybe he is shot down and you have to heal him or something (not sure if that is possible) --- Welcome to GameFaqs, home of trolls and grammar nazi's.