The sad truth is that most Wendy's restaurants in the United States of America are open on Thanksgiving Day! Most Wendy's are open from 8am-12am on most days of the year and some are open even later than that. They tend to adjust their scheduling around the Christmas holiday; but Thanksgiving is fair game--no pun intended!
There are 50 Wendy's restaurants on Long Island and I believe all of them will be open on Thanksgiving Day. The website doesn't indicate one way or another but I know all of the ones in my area are always open on Thanksgiving.