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I've been accepted to Emory and George Washington. I was leaning towards George Washington. I've now learned I'm not allowed to work at any US federal agencies and that most of the Big Law work in DC is government related. Does this hurt my employment prospects? Would even private law firms in DC downrate my application for not being a US Citizen, or for not having externship experience at government agencies? Is Atlanta a better market for corporate law?

You don't need to be a US citizen to do regulatory / government enforcement work in a law firm unless a security clearance is required. However, if you don't want to be at a law firm long term then exit options are limited because the feds are by far the biggest non-firm legal employer in DC. I have no idea what employment prospects are like for Canadians in Atlanta.

Corporate law is different than regulatory law. If that's what you are interested in, try to target NY when applying to law firms because it's the easiest market for foreign nationals to enter and the biggest corporate market.