To add on to Matthew's post in - if you feel it's a "locals only" situation, in addition to omitting your address you can always get a free phone number from Google Voice of the local area code in the city you're trying to work. This tactic could be seen as a bit underhanded by some employers, but it wouldn't be difficult to put a positive spin on it and sell it as a demonstration of just how serious you are about relocating.
Though what if that employer asked you to come in for an in-person interview? What would you say?
"Let me start by saying thank you for the interest; being considered for the position at your company is extremely flattering. Now that we're able to have a discussion outside the confines of my resume I should clarify that I'm in the process of relocating to X from Y. I'm several steps into the process and expecting to be settled by Z date. In addition to A, B and C a fourth step I've taken for the move is acquiring a local phone number, though please pardon any confusion on my current location. Until I'm settled I'm available immediately for a phone or skype interview, however if an in person interview is preferred I will make myself available in person. Thanks again for your interest and I'm looking forward to the opportunity to interview with your company."
Now - for that to work you've actually got to be seriously willing to relocate pretty quickly, and willing to get to an in person interview if they ask for it. It's a little bit underhanded, sure, but it's not a lie (so long as you never say you actually ARE local). The job market is competitive, take any [ethical] edge you can get.