I am a rising senior in a well regarded Pittsburgh area public school. When I enter college next year I will be majoring in Physics with a minor (possible double major) in Computer Science. I would like to eventually be involved in research at a major institution and plan to get my PhD in Physics. Though I am applying to big-time schools such as Chicago, Cornell, etc. and think that I have a fairly good chance of getting in, the funds to send me to such places are in doubt. I have been accepted to the University of Pittsburgh (honors college) and Case Western, both with sizable merit scholarships, these are what I consider to be my backups. I am aware that both of these school's physics departments are good, but not phenomenal. My question is, if my top tier schools don't work out for me, would high-level grad schools look down on an applicant from one of these schools or someplace similar? Would being affiliated with a 2nd or 3rd tier undergraduate program hold me back moving froward in my physics career?