The Violet Eye
The Violet Eye is the main faction that involves Karazhan. Every mob in Karazhan will give you reputation from Neutral all the way to exalted. The main hub for The Violet Eye is located right outside of Karazhan. Each mob that you kill in Karazhan will give you roughly 15 rep, the bosses will give you more reputation. If you're grinding this reputation at level 80 then you will be able to solo a decent amount of Karazhan, with a few friends all of it.
If you've never done Karazhan before or never got the key for it then you will need to do the two quests outside of Karazhan first. For a link to both of these quests click here.