Many traditional schools offer entirely online programs. It is called distant learning and some schools including one public university in Maryland specialize in it. A degree earned from distant learning courses is identical to one that a student earned from attending class on campus every day. There's no need to choose between online schooling and a traditional school.

IMO, if your going to spend all the time and money on a degree, go for a degree that is worth something in the workforce. There are many jobs that only care about a degree, any degree, but there are many careers that will pay you very good money for a degree in a useful field (such as computer science, engineering, chemistry, business etc).