Just remove any location information from your resume. Mine has none. No address, no office locations. All sorts of recruiters have called, assuming that I live in SFO or Seattle.

I don't agree. Not me personally, but company policy strongly prefers local candidates that can come to the office every day. Well, some day at least, for the last 1.5 years nobody has been required to do so. So when I read an application with no mentioning of location or somewhat convincing willingness to relocate that's automatically a no go. Well, in case of an exceptional applicant we would ask. But exceptional candidates are ahem... exceptional. The question was about normal mortals just having graduated.

Name, email, and a local number procured through Skype or Google Voice is the way to go.

True, but I think you can use this bias to your advantage in some ways in the remote world. On a resume what catches your eye first, the name/locations of the HQs of prior employers? Or home address of candidate? The former is much more striking to me personally. If I've seen someone has ever worked in my city, I mentally frame them local even if I later see their address is remote.

Point being, if you can break into the market and rack up a bit of experience, you get that some of that local bias for yourself.