Should you go to a better school even if you really like one that isn't as well known?

I have the grades, the recommendations, ACT score, and the extracurriculars to get into one of the ivys. For ever I wanted to go to Yale. Given my financial situation it seemed unrealistic to go to an ivy so I started looking around WI (where I live) to find good schools that are more affordable and I found that UW Madison is a really well known and good school. I heard about Michigan Tech through some of the kids at school and since it is an engineering school, I went to check it out. Upon walking on campus I knew I wanted to go there. That didn't happen with my campus tour with Madison. I am completely in love with the school but it is not as well known. Should I not go to MTU because it is not well known or should I not care? In case it matters...I want to major in computer science or information systems.