Not that it matters, but I'm sort of a political junky and Sen. Joseph Biden, Jr who is a f-ing rhetorical rock star went to Syracuse and received his JD. He worked in private practice and ran for local government, within four years of graduating he became a US senator and has been there ever since '72. He's a rock star. Point being, the first couple years out of school the name helps, but after that its about personal drive and ambition. Are you a rock star or a dud? If you are a rock star, you'll be one no matter where you go to school.
Also, some schools in the top 20 are regional. There are plenty of postings on regionality, so I won't go into it, but I wouldn't count on a syracuse JD going well beyond NY. Its possible I suppose, but it will be much much harder than if you just go to a school in the state you want to live in.