Top Law Schools

UGPA 3.62
LSAT 163
Undergrad at UConn, from the Northeast.

Both Fordham and Boston College have offered 20k per year. Fordham has a higher cost of attendance (roughly $80,000 vs 68,000).
I also expect to get some need based aid, though not much.

I was also offered a full tuition scholarship at American. I have family that works in DC and know the area somewhat and would not mind being there.

I have been leaning towards following a career in big law and BC and Fordham seem to be my best bet, however, American's international law success is interesting to me.

I will be paying for most of law school with loans and a little bit of help from family. I also haven't attempted to negotiate scholarships yet with any schools, I am unsure whether or not playing BC or Fordham against each other is possible as they gave me the same $$. I was also given a full ride at Northeastern although I'm unsure if letting BC know about this will have any impact on my scholarship money.

Which school should I attend?
and any advice on negotiating scholarships?

If big law is your goal, I'd say BC for sure. Check out the ATL rankings, which are driven by outcomes like employment. BC is #16.

Did you take the LSAT 3 times? That gpa will play at the t-14 and qualify you for substantial scholarships at BC, Fordham and similar schools if you reapply next year with an improved score.

If you are interested in "international law", do some research on what kind of international work you want to do (humanitarian aid, global finance, etc) and try and get an internship/job in that field. Odds are you wont need a JD. Live with your DC family if possible to allow you to take something unpaid or low paying that provides good experience. International law is a pretty vacuous term used to lure in undergrads, so you might want to nail down exactly what you want to do.

There are plenty of LSAT review courses in DC. I know you probably spent a lot of time and money applying, but you could do a lot better with only a 5-7 LSAT score increase.