If your child was planning on going straight in to graduate school to pursue a course of study, then consider attending a local college (CUNY or SUNY even) for four years and save your money for grad school. College is 128 credits. Grad school is considerably less. A college diploma is a college diploma.
Ivy League schools (and those like them) will just suck you dry in your finances, just so you can have a name on a piece of paper, which may or may not mean anything to you in the future.
Very sound advice provided that you achieve a high GPA and can get a good score on the GRE. When you are ready for grad school, find the schools that have the best reputation in your field, apply and seek a TA position or other financial benefits and charge on. Networking with some of the grad school's graduates and professors doesn't hurt either.
I went to one of the better SUNY schools. Very well respected in terms of getting into grad school. If you plan on staying in NYS, definitely look into SUNY. Out of state, however, there is not much name recognition.