How do I find out what the average rate Registered Nurses get paid in my state for permanent positions?

Check Glassdoor. You can look up average hourly rate by facility, by specialty, and by years of experience.

I started interviewing at hospitals in my desired area to get real time data. That way, you can find out the average hourly rate for your area for your level of experience

Check if your area has any union hospitals. The wages are usually in the contract. Can help give you ideas of what to expect.