About ten years ago, when I had no insurance and needed free testing, this was the one place in Boston I found to do it:

http://www.bmc.org/infectious-diseases/services/STD-HIV-testing-treatment.htm

Planned Parenthood would also have been an option if I could show them evidence of low income, in the form of regular paychecks, which they could use to access subsidies for low income people. But since I had no regular job at the time, it turned out too complicated to do anything through them without paying for it. Boston Medical didn't need anything, it was just plain free.