pslawnet.org is a great database of public interest jobs. I also recommend looking through the list of organizations and sending them a cover letter + resume even if they don't have a recent job listing--that's how I got my summer job. There are also non-legal organizations on there, but some may be working on a project that is law-related that could use an intern. It's worth a shot if you are interested in what the organization is about.
I also found some good ideas by looking through lists of past recipients of my school's summer public interest fellowships. My law school's website just had pdf files listing the recipients and stating where they worked. Some of them also had good descriptions of the duties and what the student though about the experience. That way you also know that the organization has hired from your school before.
And a general internet search can be useful. If you want to work in Atlanta, for example, google "Atlanta public interest law" or "Atlanta nonprofit" or "Atlanta domestic violence" or "Atlanta low-income legal" or "Atlanta pro bono" and you should find plenty of public interest organizations that could use a law student intern.
It depends on the school, but your Career Services Office might have good leads on public interest positions.