Take the coordinator job. IMO, any RN experience is better than no RN experience.
Think about it. Yes, the patient care coordinator is probably not acute care experience.
But a year down the road, you could be a nurse without acute care experience but with a year's RN experience in healthcare, who has developed some skills, who has had the opportunity to network and make her name be known, who is building a resume, who now has professional references in healthcare that she can use when searching for work, and who can also use this time and her income to get certifications, take continuing ed classes, join professional organizations, and otherwise improve herself and her chances...
Or a year down the road, you could be a nurse without acute care experience, but without any nursing experience period, with little to no skill development, with a gap in the resume that needs explaining, with limited opportunities to network and probably without healthcare references. Employers get edgy when they see long gaps of unemployment and wonder why. And let's face it: a reference from a nursing school professor loses its influence the longer it's been since you graduated.
Now, when the acute care job decides to look at your application a year later (though hopefully sooner than that), which nurse do you think looks more appealing to them?
This coordinator job doesn't have to be forever. And no one says you can't keep looking for acute care positions while working. You may be able to find something acute care that is per-diem and get the best of both worlds.
And last but not least: you don't have to work in a hospital or in "traditional" nursing jobs to be a nurse. You became a nurse when you passed the NCLEX. No one can take that away from you. Sometimes I think new grads, in their "hospital or die!" quest, tend to forget that.
Best of luck whatever you decide!