Directions to Priority Urgent Care in Unionville, CT Now Open! Get Google Map Directions to 45 South Main Street, Unionville, CT 06085 Hours: Mon – Fri: 8AM-8PM, Sat – Sun: 9AM-5PM Call: (860) 470-7710 Appointment Requests Priority Urgent Care and Walk-in Clinic in Unionville CT is right by the Farmington River, and a short drive away from nearby areas of Farmington, Avon, Bristol, Burlington Connecticut. Call Clinic Specials Patient Reviews Open Hours Directions Patient Feedback Appointments Visual Tour Back