Any professional organizations would be a great way to spread the word. However, it doesn't have to be specific to project management. Lots of organizations and companies have project managers, and we're more likely to get better, more realistic questions from people who work as real project managers in real companies.
The one possible problem with PMI-centric organizations is that they may bring in people who are too rigid. I was accused earlier of being more of a technical lead than a project manager and that my question was irrelevant. At my company, a project manager is technical and does more than just typical PM tasks. I'd hate to see the site become inflexible because a particular project management task doesn't fit the PMI definition of a project management task.
The job descriptions for a project manager will be different from company to company, and the site needs to be flexible in order to accomodate the majority of project manager roles.
UPDATE: Here are some other ways that we can promote the site: