Figure out which Group you're in:
Sign up for the Duke waiting list:
https://www.dukehealth.org/covid-19-update/join-waiting-list
They will contact you with openings. This is how I got a Jannsen (Johnson and Johnson) vaccine.
Check the UNC Appointments Regularly:
https://www.unchealthcare.org/coronavirus/vaccines/phase-1b-covid-19-vaccine/
There will often be a message on there staying "We’re very sorry, but all vaccine appointments have been scheduled", but when there's not, you answer a brief questionnaire and then see which vaccines are available and where. The slots get snatched up quickly, and sometimes they're hours away.
Check Walgreens Regularly:
https://www.walgreens.com/findcare/vaccination/covid-19/location-screening
They do it by zip code, so you might have to enter a number of zip codes before you find something near you. If you're willing to drive a ways, try a variety of nearby codes.
A Note on the Experience
Other people’s experiences may differ, but I was not grilled on my “eligibility” for Phase 3b. I just filled out the answers to the survey when trying to find an appointment online, and then when I got to the appointment, all they did was confirm my identity (photo ID, name, birthday, allergies) and give me some general info on the vaccine before they jabbed me. In general, don’t feel “afraid” to make an appointment. If you answer the questions reasonably, step through and get your appointment, you’re not going to get in “trouble” for signing up in the wrong phase. It’s just a way of helping people line up in an orderly fashion, not a punitive system that will be audited and scrutinized. Read the questions, try to be honest about your situation, and get it as soon as you can!