If you live in Northern Virginia, then you have an option of going to UVA at a bargain price of $12,000 tuition ($25,000 less than for out of state residents) per year. At Penn there are about 10,000 undergrads and at Cornell and UVA there are just over 14,000. You will receive the same type of education at all three universities, which are similarly sized at just over 20,000 total undergrad and grad.
Unless you have some specific area of interest like for example computer science or engineering, where Cornell is extremely well known and UVA is unknown or very weak, it makes no sense for a Virginia resident of your family's means to attend Penn or Cornell just for a marginally better name. Most certainly, neither Penn nor Cornell will knock $31,000 off their $43,000 tuitions with merit aid to match the UVA price tag.
With Dartmouth, you have a different situation. First and foremost, Dartmouth is a liberal arts college of 4000 undergrads. It's not a research university. You are likely to get smaller classes, particularly in the first and second years. Secondly, Dartmouth has a higher per student endowment than Penn or Cornell. This may translate into your incurring less debt than you would at Penn or Cornell. It also has the D-plan which requires you attend at least once during the summer, so that not all 4000 undergrad are on campus at once. Thus, Dartmouth offers a different type of experience than a large well-known research university and you'll have to decide if that's what you want.