Top Law Schools

I want to become an ADA in a large city( NYC, Boston, Chicago, or DC)

Does one need to go to law school in the particular state where the DA’s office is to have a good shot at getting and internship/job?

If I went to George Mason or Richmond Law, for example, would I still have a shot at an internship/job in NYC or Boston?( DA’s office)

You don't have to, but I think it can help. Because people often do end up working where they went to school (especially when you're talking about somewhere like George Mason or Richmond, as opposed to, say, Harvard), alumni networks are strongest locally, and I think alumni networks can be extremely helpful for DA jobs. Like the Suffolk County DA's Office in Massachusetts is going to be full of BU, BC, Suffolk, and Northeastern grads. Not saying at all that they're going to reject a good candidate from another school, but the local grads are going to have a "know quality" going for them that you don't.

The other advantage of going to a local school is that you can do school-year internships with offices where you'd like to work, not just during the summer.

But it's definitely possible to go elsewhere, if you do all the right things to make yourself a strong candidate.

You should go to school in the location you'd like to practice unless it is a T14 or something, or you're from NYC but went to like Wake or ND and now you're trying to get back home.
While DA/PD offices aren't the most selective, there's a big pull for taking local folks; at least, that's the case for my market.

I don’t know anything about huge jurisdictions like NYC or Boston. But my ADA friends all over the country report being desperate for lawyers. It’s always been weird to me when folks are indifferent between, say, NYC and Chicago. In this context you could probably get into either DAs office from any top 50 school-but, say, Loyola v CUNY would depend where you want to go.