There are lots of assignments for Psych RNs accross the country. I am constantly getting emails for Psych assignments. In my experience just about every company recruits Psych RN's with a small percentage of exceptions. I know there are couple of companies that say they specialize in Psych but I found this not to be the case as they staff many other specialties as well along with a good supply of Psych assignments.
Since Psych assignments are not AS abundant as other specialties it is even more neccessary to register with a good number of companies as well as work on an assignment with several companies. On top of that stay in email contact with other recruiters. If you do that you will see that many companies may be marketing the same assignment but also different ones you haven't seen. Psych certification helps as well.
Also most importantly is a knowledgeable, fair. effective/efficient recruiter working as a team with you (as with any specialty). Once you sign up with a company and get stuck with a poor recruiter it is difficult (not impossible) to change recruiters unless that recruiter leaves or is promoted to management. Keep in contact with great recruiters via cell as I've seen many great recruiters move from company to company.
Also save up those $'s because to give you confidence to hold out for good paying assignments and when you are looking have 2-3 potentials going as they fall through many times. The more state licenses the merrier and look outside of just Travel Nurse Companies, look at Seasonal, Military Contracts , VA, per diem (with or without a contract), and even the Dreaded!! Perm although its best if you stay with inpatient Psych as the vast majority of Psych Travel is inpatient psych although I've seen Psych Home Health, Psych Management, Psych Case Management here and there. Good Luck :)