Haha, I want to do women's rights PI after lawl school, too. I've worked at a number of women's rights nonprofits.
Like other posters have said, it is much more likely that you are going to get an unpaid internship than an actual job, especially being a new college grad. Have you worked for/volunteered for any women's rights groups in the past? If not, I would set aside a few hours a week now to do that - it is going to make looking for a job/internship a lot easier if you have already displayed a commitment to a certain issue/have references that can speak to your dedication AND abilities.
Working for the ACLU would be great - it is, obviously, an amazing organization that would give you great connections in almost any progressive nonprofit you can think of. I don't totally agree with other posters in that any nonprofit will look the same. Showing a long-standing commitment to a certain issue is going to give you an advantage when applying for PI
jobs after law school, will give you connections to people who work in nonprofits you want to work for
after law school, and will give you a lot of insight into where you want to work after school. Getting a PI job
after law school is a lot different than getting a big law job.
As for applying, send cover letters and resumes to nonprofits you want to work for - like other posters have said beggars can't be choosers, etc. Apply broadly, but there are dozens and dozens of women's rights nonprofits in NYC. You are going to get a lot more responses when looking for an unpaid internship vs. a paying job (if that gets you any at all).
As far as admissions, yes, +.1 on your GPA or 1-2 points on the LSAT will make a much bigger difference than any job.
