In CT, within 45 minutes of Avon...
Budget Public--Pequabuck GC; Bristol, CT (about $40-45 in peak times)
Big-bucks Public--The Ranch; Southwick, MA ($115 peak)
Private--CC of Farmington; Farmington, CT
In VA, within an hour or so of Lexington...
Budget Public--Lexington G&CC; Lexington, VA
Big-bucks Public--Old White course at the Greenbrier; White Sulphur Springs, WV
Private--Ballyhack; Roanoke, VA
In SC, within an hour or so of Pawleys Island...
Budget Public--Indian Wells GC; Surfside Beach, SC
Big-bucks Public--Caledonia G&FC; Pawleys Island, SC
Private--Wachesaw Plantation; Murrells Inlet, SC (I've not played Bulls Bay)