Which zone do I need to be in for specific Mayhem missions?
The mayhem you get is based on your level, not on the zone you're in.
http://www.fimfiction.net/story/36641/My-Little-Exalt
If you mean you've out-leveled them and looking for lower level teams to join, then the break down of which Mayhem = which level range is here:
Paragon Wiki: Mayhem Mission
(edit to add: the list of the level ranges of the Villain zones can be found here : Villain Zones )
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"Chew Electric Death, Snarling Cur!"

Do I need to be in Mercy for Atlas and Skyway?
Exactly where must I be to get to specific areas? I'm trying to go for the Invader Badge.
Can anyone give me a few details on where I'll need to be to join a team?