Enfield Care Center. Directions To Our Enfield Care Center: 113 Elm Street, Suite 303, Enfield, CT 06082. Phone: (860) 253-6867 Fax: (860) 741-4399. From I-91 North. Take I-91 North to CT-220/Elm Street, exit 48. Turn right onto Elm Street. Take a left at the second light. (Denny's is on the left, Burger King is on the right..