It doesn't matter a lick where you go to law school. I can't think of any race that seriously hinges on where you went to school. Certainly some electorates are more averse to carpetbaggers than others--If you want to run for office in Mississippi, but have never lived there growing up, and went to UG and LS in different states, and worked in NYC, then try to run in Mississippi, they'll laugh at you. But as long as you have a credible claim to the area, you'll be okay.
Of more concern than upsetting the electorate/populace for carpetbagging would be not getting respect from party elders and donors on account of your carpetbagging. You need help from them if you have a shot at winning any partisan office (at least in a district that isn't already 70%+ in your party's column), and if they don't know who you are, they won't feel compelled to help you.
Assuming you settle down in some place for at least a couple of years, then once you start running for office, chances are nobody will make much of your non-local roots and education. And if they do start to stick you with that, then it means you're doing something right, and that's all they can find against you.
My advice: go to the best law school you can. Practice BigLaw in NYC (unless you figure out before then where you want to settle down; if so, opt for the best firm you can in that state's biggest market) for long enough to pay bills/meet a woman/get satisfaction/get bored/whatever. Move to whatever state you want (unless you're already there), and try to move into an area/district that votes with your party. Get a job with a firm that will let you be flexible with your hours. Then start to meet people, beginning with the chair of your state and county party organizations. Tell them that you want to run for office in a few years and ask how you can get involved. Figure out who some up-and-comers are . . . such as a young assemblyman everybody likes or the Insurance Commissioner who is just biding his time before he runs for Governor and Senate . . . and then offer to help their campaign. A great idea would be to offer to do their legal work pro bono. Campaigns are strapped for cash, and if they can have a friendly well-educated lawyer work for them for free, that beats the hell out of having to put an attorney on retainer. Build friendships with these candidates, and also their staff and consultants. Figure out who's who. Who are the top donors in each county, who are the activists and what are their pet issues, which consultants do your party's candidates use, etc. Meet them and befriend them all. After a few years of meeting everybody you can, and getting a lay of the political land, then start your path towards world dominance, beginning by running for State House or Senate or County Commission.