I'm biased since I love my alma mater, but I chose UVa Law because of their repayment plan for PI attorneys. Since that time, they've become even more public interest friendly. For e.g., for graduates they still have the:
GRADUATES
(1) repayment plan, where they will make all your payments until your income based repayment debt is forgiven in 10 years. The stipulation is that you need to land a PI attorney gig within 2 years after graduating.
They have also stepped up their game for PI attorneys in other areas--FYI I was lucky to be able to take advantage of the fellowship (which was really helpful since a life crisis during law school meant I needed to move to a new area and leave my networking opportunities developed during law school behind):
(2) Kennedy Fellowship: I'm not sure that this only applies to PI attorneys, but the law school will pay you a pretty great stipend for a year after graduating to work in government/PI organizations. This allowed me to move, get involved with another public defense office, make an impression (I won two cases that were considered lost causes), and get hired.
(3) Bar Exam Stipend: They have a stipend for graduates that will pay for their bar exam course and bar exam fees.
DURING LAW SCHOOL
(1) Guaranteed Summer Funding: When I went to UVa Law, you applied for PI summer funding through a PILA grant. Now all PI minded students can get funding for their summer positions, which is incredible.
(2) PI On Grounds Interviews/Career Center: While I didn't find the career center, which has a PI focused section, entirely beneficial to my PI job hunt, I know that many did. First, they invite many PI organizations to interview PI students--and there are definitely plenty of organizations that participate. It looks like they also have a list of organizations that are willing to take PI students right out of the gate upon graduation through the Kennedy Fellowship. Also, throughout the year they are constantly sending emails to students concerning projects that need student researchers, volunteers, from PI and government agencies. There is a great network through UVa Law on top of it all that can be utilized to land a PI position in some really great organizations.
(3) Clinics/3rd Year Practice Cert: UVa Law has some really great clinics that let me get litigation experience during my 3rd year. I obviously participated in the public defense clinic, though there were many other clinics with public interest work. The clinic was ran by this very helpful Federal PD. We were assigned different criminal defense attorneys who did a great job serving as mentors throughout the process. We were each given cases that were likely to go to trial, and so on top of the summer work I did, I ended up practicing in two different jurisdictions during my third year in this clinic. This clinic helped to clarify the approach, the laws, and the in court ins and outs better than my summer clerkship--which, in many cases, was like the wild wild west [lots of big assignments, but you were generally just hanging on for the ride and trying to figure it out as it was assigned].
GETTING IN
It's no secret that UVa Law has the early enrollment (though you have to accept if they take you) option. I took advantage of this and had similar stats to what you have [166 LSAT + 3.95 GPA]. Though my LSAT was at their absolute low end, I'm convinced that they considered my GPA a lot more because I wrote a solid personal statement that also explained that I wanted to practice public interest law, why, and how my life experiences would be a benefit to the people I wanted to serve. I also overnight Fed Exed my application on the first possible day I could (since they have more leeway to accept reaches before they fill up the seats). It was a Friday. The following Monday, I received a phone call and was accepted.
Overall, UVa Law does have a soft spot in its heart for public interest minded students. It's important to the school that the public interest point of view is represented in the classroom, and carries on
after law school, because it's valuable to the UVa Law community--and they put their money where there mouth is on that. If you can write a compelling PS, that demonstrates your intelligence and commitment to public interest, you can overcome your LSAT score.