All sorts of great advice from Karen Kelskey, PhD, on getting a job in academia and beyond at The Professor is In: theprofessorisin.com – her facebook page also has a lot of great advice and the occasional free webinar.
Association of Science and Technology Centers’ Job Bank (be sure to check through all the categories at the top of the page)
North American Association of Environmental Educators’ jobs (does include everything from entry-level on up – check out the featured jobs for sure)
Society for the Preservation of Natural History Collections
Association of Zoos and Aquariums jobs (nope, they don’t use “aquaria” as their plural)
AAAS Policy Fellowships for early-, mid-, and late-career science PhDs (engineers don’t need a PhD)
AAAS Mass Media Fellowships for grad students and postdocs
Actually, a whole list (from April 2017) of fellowships for scientists, as part of a whole fellowship site
A whole listing of science comm/science writing fellowships (paid!)
Friends of Joe’s Big Idea and NPR Science Communicators
Turn your PhD into an Industry career with https://cheekyscientist.com/
International Fellowships such as Fulbright Awards for faculty and Fulbright fellowships before your doctorate, awards from individual countries (France), and through other mediator organizations.
A whole host of local/state museum and other organization sites, such as:
Florida Association of Museums
State Science Policy networks are starting to crop up, such as California Council on Science and Technology (they have policy fellowships)
Cooperative Extension opportunities tend to be listed by state through the home university, such as: UF and FAMU in Florida
Other policy job ideas:
Working for a campaign (maybe unpaid) or elected representative as a science policy advisor