Good hospitals for a first timer?

Wyoming is friendly!

Unfortunately, every unit on every hospital may be very different, and the politics can change over years. So it is not really possible to suggest a hospital with any assurance. What you do need for a first assignment is a traveler friendly environment and interviewing a bunch of recruiters should land you a couple that you can trust to have the same goals as you (your best interests at heart) to steer you to a successful first assignment that is not merely chasing big bucks or a hellhole.

General advice about good places to work (often better paying as well), are unionized states like the entire west coast, much of the NE, and some of the midwest. Such places have staffing ratio rules (the law in one state, California), and better working environments generally.

DOD jobs are usually just with one winning contractor. I'd search on Google for DOD travel nurse jobs and go from there. I've occasionally run across a web citation of who has the contract, but their sites are often unclear. Good luck! But I think DOD assignments (and VA - who runs their own travel company) will take a lot longer to get than ordinary travel assignments.