I don’t know what it would take to convince your parents, but William & Mary is really a great option for people who like colleges such as Yale.
William & Mary is actually older than Yale (second only after Harvard), and it has a really historic-feeling campus, but with modern facilities. I really like Yale’s campus (including because I like Collegiate Gothic), but William & Mary is one of my other favorites.
Also like Yale, it has long been among the favored colleges of US sociopolitical elites. Again also like Yale, it has maintained very strong departments in core humanities and social sciences, while also being quite good for natural sciences, and increasingly some tech stuff too. William & Mary grads are definitely employable!
In terms of undergraduate size, there are about 6800 at William & Mary, 6750 at Yale. And actually, like Yale, William & Mary is basically a coastal college, with good access to beaches and the ocean.
OK, so given all this, why isn’t William & Mary, say, an Ivy League college?
Well, a variety of reasons. For one thing, it was too far away to play football regularly with Yale and Harvard back when they relied on team buses and there were no modern interstate highways. For another, William & Mary ended up affiliated with the state of Virginia (long story behind that–and at one point Yale was sorta headed in that direction with Connecticut, but then backed out). For a third, it is an R2, not R1, research university, so while it does have grad programs and professional schools, some quite good, it is not an R1 like Yale.
OK, but still, William & Mary remains a very popular undergrad option among the sorts of US families who also look at Ivies and such. And while I actually think a lot of these virtues are shared with some small independent colleges, aka LACs, William & Mary is not that small, and it is in fact a university.