I'm visiting the east coast to visit a few colleges and their labs. I am planning to apply to graduate school. I want to know if I can tell the border patrol officer this if applying for entry under the VWP?
You have two options:
Enter visa-free, visit the colleges (which is allowed), then apply and return home to obtain an F-1 visa, with which you can re-enter.
Get a B2 "prospective student" visa, with which you don't have to exit and re-enter the US, but can apply for a change of status, which however costs $370. The next time you travel abroad (except to Canada, Mexico, Bermuda or the Caribbean for less than 30 days), you have to get an F-1 visa from the local US Embassy before re-entering (make sure to have your I-20 for this)