Your mum is right in terms of reputation. Drexel has a good rep in the design field - it's known for its design programs. CW Post is not known as an art school.
But you're right in terms of fit. If you feel that Drexel is too far away, you're probably right.
The fit needs to outweigh the reputation.
That said, what others said is correct. In graphic design, it's not necessarily the school you go to, but the portfolio of work that you have, which will get you jobs. Although, if you go to one of the top schools, it can help get you in the door, it's still the portfolio that's going to sell you.
If you feel CW Post is a better fit, so long as they offer the major you want, go there. It's a decent school. While you're there, make sure you do things to build your portfolio and your experience, so you'll be employable upon graduation. Do co-ops, internships, and volunteer work in your field, both on campus and off. Take advantage of every opportunity to build that portfolio, and to build a network of contacts in the field, and you'll do better than most upon graduation.
Make sure you take some courses that teach you computer skills, because they'll be very useful in design. It may also help if you learn how to type, because that helps you do some of the work more quickly.
If you're still open to applying to other schools, programs that might appeal to you may include:
-The Pratt Institute
-School of Visual Arts