I need help with when and where to apply

I am currently living in Cleveland and have been getting information from you lovely Texas nurses for the past couple of months Very appreciated. Anyway, I am deciding between three apartments--one in Grapevine, one in Irving, one in Fort Worth. I will be moving beginning of July, my question is when should I start applying for jobs? I don't want to apply too soon and irritate them by not being able to start for months, but don't want to wait for the last minute. Would applying 2-3 months before my move date be a good timeline? Any opinions on this would be helpful. And I am in the process right now of getting my Texas license now.

By the time I move, I will have 2 years exp. as an RN (BSN) with skilled nursing and med surg work. I am trying to break out of the med-surg/typical hospital setting. My three big interests are child or adult psych (I had clinicals in an independent inpatient psych clinic and would really love a setting like that!) public health/school/community nursing, and long term care/alzheimer's setting. I have been doing some research finding these types of jobs, but any help about places you've heard that are good, bad, or other places to look for these jobs would be really helpful. For public health jobs, I've looked at different counties' board of health websites...any other ideas?

Sorry for it being so long, I really appreciate your help though!!