Full disclosure: I am a UChicago grad.
For regular corporate, gov't, and PI jobs, schools ranked 4-12 are going to be roughly equivalent for job prospects. There is some dropoff for the very upper reaches of those jobs and clerkships, but not a ton. You see a lot of Georgetown grads around, but that's as more of a factor of giant class sizes than of equal opportunities. There will be more competition there. Don't go to Notre Dame, Emory, BU, or a regional school since you have significant T14 scholarships. You can certainly be successful coming out of those schools, but you would be under pressure to perform in order to have access to the same opportunities that flow like water at T14 schools as long as you're not at the bottom of the class. For example, in my biglaw class every T14 was well represented while there was only a sprinkling of T30.
Given that information, I think it's a no-brainer to go to UVa since it's the cheapest of the 4-12 bunch and has great access to clerkships and the DC market. UChicago is not worth $110,000 more than UVa in any universe. A few things to note...
1) Within that 4-12 range, pay A LOT of attention to cost. I was lucky enough to get a full ride to UChicago, so after 5 years I was able to change careers (liked law school, didn't like the practice of law so much) and had enough money to pay for another year of grad school, the downpayment for a home in a VHCOL area, and have a nice chunk of retirement savings left over. I have friends whose net worth was just getting back to zero after 5 years of working in biglaw. There is a lot to be said for giving yourself that flexibility. I still wouldn't go to ND, BU, or others for free vs. T14 at half price, though, because you are unnecessarily limiting your options geographically and job-wise unless you are close to the top of those classes.
2) The odds you end up going into something like 1st Amendment law is vanishingly small. Declaring such intentions when you arrive on campus will draw a knowing smirk from 3Ls. Such jobs are in very short supply and generally require sparkling resumes, including a high ranking at a top school, a prestigious clerkship, and getting hired at a boutique DC firm, with perhaps a prestigious government job or two thrown in there for good measure. That's great if that's your goal and I have former classmates who have their dream jobs (e.g., one is chief of staff to a senator while still in his early 30s, a few others parlayed Supreme Court and top-tier federal clerkships into practicing constitutional law), but they were rockstars and I would be realistic about the odds of it coming true. In the end, almost everyone ends up in biglaw before fanning out to a wide variety of jobs and other careers, few of which are probably as interesting as what they dreamed of going in to law school.
3)As for culture, UVa and UChicago are noticeably more conservative than every other T14 (that may be good, bad, or neutral depending on your point of view). Conservatives are still outnumbered by liberals at both, but there is a difference between their culture and that of other schools. There was still lots of good rapport and bonhomie at UChicago regardless of political affiliation, however, and of the (admittedly few) conservative friends I have, most date from that time.
4) If you go to UVa, practice popping those collars!
As an aside, and despite the fact I think it should be near the bottom of your list, I feel the need to defend UChicago from all the hate on this thread
1) After working with graduates from every school imaginable, I didn't find UChicago students to be any weirder than others (of course, perhaps my own weirdness prevented me from seeing it...). I came from a very typical undergrad atmosphere (not-highly-ranked state school more concerned with football than academics) and probably spent more time at rugby parties than studying, so I'd like to think I'm well-equipped to judge UChicago on this metric. I think this misconception is more a product of confirmation bias than reality.
2) Although everyone does joke about it being "where fun goes to die," I doubt the experience is any different than any other school. That basically means a really stressful first year followed by an easy last two years full of interesting seminars and whatever classes interest you. I think both the weirdness and fun thing are more applicable to the undergrads than the professional schools.
Good luck making your decision! You have some great options!