Unfortunately, I do not think any school in the Northeast with a track record of grads getting into investment banking will fall within your budget.
One possible exception is Baruch College, which appears on one of the feeder lists referenced above, but that is a commuter school and I don’t think it has a big advantage over UT-Austin or A&M.
I really think the Texas schools are his best bet. If he is concerned about getting into the program he wants, he could look at Brigham Young or Arizona State which are both on the investment banking feeder lists attached above and might make it within budget.