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I have a 20k scholarship at Northeastern and was recently accepted off the waitlist at GW with no aid.
Is the extra debt worth it? It'd be approx an extra 25k/yr.

It depends on your career goals. Most will tell you not to take sticker outside the T14, or even the T6 or T3, but you have to compare what you want to do with the debt that you will have. There's no doubt that GWU is a better school, but if you're okay working in the area around Northwestern, it might not be a completely horrible choice. I would advocate retaking and reapplying if you can't get any more money out of GWU (I'm in a bit of a similar situation). I think it's tough having 200K in loans from a decent, but not top-of-the line school, but without knowing your career goals, I can't say whether a T2 near many strong T1s is worth it either.

Personally, I would do neither. But if you have to choose, then it's GW. IMHO, I wouldn't even go to GULC or Cornell at sticker.

Neither. GW isn't worth sticker, Northeastern is low on the totem pole in a small market.