Why mentor FIRST FRC in college when you can pour your time into
building your own robots for your own competition? This is especially true if you can afford out of state tuition.
Undergrad research benefits you, both in curiosity and in career, quite a bit more than robotics mentoring will. If you're going to let something influence your decision, IMO you should let the research influence you and mentor 'on the side'. That said, Virginia Tech does have a local team, FRC 401 The Hokies.