List of reputable open access journals
The Directory of Open Access Journals (DOAJ) is an attempt to create such a list for all fields, including the social sciences:
DOAJ is an online directory that indexes and provides access to quality open access, peer-reviewed journals.
They have a search function that lets you drill down to specific fields.
I would suggest going about this a slightly different way. The reputation of journals derives from views of scholars in a particular discipline. There are many closed access journals that are not very reputable and many open access journals that are reputable. You can figure out the ones that are reputable by looking at three things:
- What journals are being cited in other journals of known reputation? Journals that get citations in other journals are likely to be publishing decent research. This is not a guarantee, of course.
- Who is publishing in the journal? Reputable scholars tend to publish in reputable outlets. If a journal has prominent scholars publishing good work there, it's probably a decent journal. This is not a guarantee, of course.
- Who sponsors and publishes the journal? Reputable journals (especially in the social sciences) tend to be published by or endorsed by scholarly associations. This is not a guarantee, of course.
Thus, rather than trying to find a list of reputable journals, think about how you would evaluate any particular journal. If you find correct answers to any of the above questions, there is a good sign it is a reputable journal since the idea of "reputation" is a social construction that reflect precisely the above criteria.
OnlineSchools.org produces a list of various open access journals. While I can't say all are reputable, most look like they point to well established and credible organizations or educational institutions.