Determining whether an OA journal is reputable requires an evaluation of the journal.
Some characteristics that indicate the journal is reputable include:
Adapted from Paul Blobaum's Checklist for Review of Journal Quality, Governor's State University
While some or most of these characteristics are often shared by reputable journals or publishers, not all of them need to be present for the journal to be highly regarded.
Many open access journals are indexed in the Directory of Open Access Journals (DOAJ). In order to be included, journals must apply and go through a rigorous evaluation. Being included in the DOAJ is one sign that a journal is reputable and a good place to consider submitting your work.
Some publishers are also members of the Open Access Scholarly Publishers Association (OASPA), which is an organization that works to maintain best practices in OA publishing globally. In order to become a member, publishers must apply and pass a strict initial review procedure. Publishers must also continue to exemplify high standards to remain members. Membership in OASPA is another indicator that a journal is reputable and a good place to consider submitting your work.