Did you check to see if any of these schools offer a combined BS/MS degree option? If you are positive that you want an advanced degree, that might also help sway your decision if it is available.
Princeton will be be the most rigorous and hardest academically of your choices and at times you might feel like you are studying, studying, studying. It’ll also have the most opportunities and resources available especially due to be so undergraduate focused. Search for the ‘Real Talk Princeton’ blog and read and ask questions. Many pre-frosh making decisions.
While I understand your worry about Princeton, if you look at the Ivy League in general they have among the highest average GPAs, and Princeton formally gave up on an effort to limit grade inflation four years ago. I do think you will fail or do poorly.
While Princeton doesn’t have grade deflation any longer they do have a lot of the professors from those days that aren’t necessarily keen on grade inflation. Natural Science concentrators notoriously have some of the lower average GPAs on campus followed closely by Engineering.
Princeton should be an easy choice as long as you won’t be homesick. GT is totally out of the picture for that price. I don’t think you can go wrong with V. Tech or UVA but Princeton would be the first choice for me. I will say all four are good schools.
Princeton
Princeton is Princeton. The others are not on the same level. Easy decision.