Out of the three, Minnesota has the best overall reputation in physics. Dartmouth and Virginia Tech are probably similar in terms of reputation. Dartmouth is technically an Ivy League university, but they're primarily known as an undergraduate university.
As far as high-energy theory goes, I'm not an expert, but both Virginia Tech and Minnesota seem to have large particle theory groups. Dartmouth's group is fairly small (which is admittedly consistent with it being a smaller school). Looking for citation counts, Minnesota leads by a long shot, and I'd put Virginia Tech on par with Dartmouth here.
Based on this, I'd say Minnesota would be my first pick. They have the biggest and most prestigious program, it seems. However, there are some other factors you should consider before you choose:
- Who's accepting new students? You should talk to some faculty you're interested in to see if they'll even be looking for new students in the coming year or two.
- How are your prospective advisors as people? This is one that you'll need to find out from people in the field. There are a handful of PIs across the country famous for their contributions to their respective fields but infamous for their poor treatment of their graduate students. An extra publication or two probably isn't worth dealing with an ogre for the better part of five years.
- I looked at each faculty member's h-index to figure out how important they are to the field, but that tends to favor older faculty. There may be some really young faculty members who are making big waves in the field but haven't had time to accrue as many publications and citations.