SUNY.edu actually has a campus list on its website. From there you can go to any of the individual schools to see which courses and majors they offer, and the minimum requirements for acceptance. The information will help you decide which schools you may like. Collegeprowler.com also offers side-by-side comparisons on its site.
Set up a visit for each of the schools that looks appealing to you. Schools always host open houses, especially in the fall and spring; most are willing to give private tours as well. Ask both staff and students questions about tuition and campus life while you're there. You may be able to narrow down your choices simply by setting foot on campus.
The SUNY schools are closely related to the towns where they're located. Therefore, checking out the town and surrounding area is just as important for your comparison as checking out the school itself. Eat in a local restaurant and talk to some of the locals about the college; some may even attend there. You may love the campus, but if, for example, you're a city person and the campus is in a rural setting, you may not enjoy the experience.