Job search in another city- how do I do it?

I think I'm ready to leave my hometown and move to the next largest city. I've been a nurse for, hmm, a little over a year and half. When I got my job here, it was really easy, because I worked at the hospital as a CNA for over a year, so I pretty much just started working as a nurse after I got my RN license. And, I got the CNA job because I was a student nurse there. So, I'm a little ignorant at job search etiquette.

Portland is about four hours away by car. I've made plans with my friend, whom I'll be living with, to go up there and look for apartments next month. I've looked at hospital websites and I see postings that would be a good fit for me, but I'm unsure of how to act. Here's my thoughts:

Should I apply online at the hospital websites, and hope for calls back to set up interviews before I leave?

Should I go on my trip without applying online, and then just visit the hospital recruiters and human resources offices, hoping that they'll have time to talk with me whenever I just show up?

Should I apply online, and then visit without an invitation, and tell them, "Yes, I've applied online, I was just checking up on it"?

Oh, and about online applications anyway: Is applying online better or worse than printing up applications and sending them off?

Is it absolutely critical to have a resume?

I know I could just call recruiters and human resources offices for more information. But what do I say when they answer the phone? How can I not sound like an idiot?

I really don't expect anyone to answer all of these questions I have in my mind, but I'd love any kind of input anyone has to offer. Thanks in advance!