If you're a new grad AND you have no previous healthcare experience, you cannot afford to be picky. Also be aware that morning weekday shifts are extremely hard to find. I was able to get my experience built up working night shifts and home health agencies. The better your availability, the better your opportunities. I signed up with home health agencies and flu clinics. Even when I work a full time job, I keep my agency and flu jobs because they build up on my resume and technically I only need to work a few shifts to stay employed with them. Plus, extra money!
It's hard being a new grad, but don't let it discourage you. Just start creating an actual career path determining what field you want to get into. Once you start getting experience in a specific area, you really start to get the benefits of finding good paying jobs easily. Imagine being a new grad LPN, which is what I was. They don't really hire LPNs in hospitals in AZ so that was really difficult. Just be patient and take what you can. I was a school nurse for a few years until I realized that I wasn't going to be able to get my foot into a hospital with that experience above someone who has actual clinical and facility experiences. And being a school nurse isn't my goal. So now I am looking for something completely different to build my experiences.
And NETWORK! Keep in touch with your classmates, get reference letters and contact information from your instructors. And from this point on get a reference letter from each place you work as soon as you get a little time in with them.