If this is not 100% the exact location, then I am pretty confident that it's across the street.
The Blue Eagle was already in its last years when we walked down there as children in the 1940s. It was down the hill from the Nemerson, a major hotel. I believe the Blue Eagle had its heyday in the 1930s and was named for socialist-related concepts.
Jan Teitelbaum: 11/1/2011 -> Blue Eagle is the Hotel that my mother met my father . He was a musician at the hotel . When I was a kid I used to sit on the white fence with my girl friend. There was a Burlesque House in the old playhouse . Farrel and I used to look through the window, and watch the show. It burned down one summer and it was never replaced. The Blue Eagle was 500 feet fromthe Pines Hotel in one direction and 500 feet from the Nemerson Hotel in the other direction in South Fallsburg . In between was my cousins Bungalo colony Grossgolds. Take Laurel ave from South Fallsburg turn onto Park PL about 500 feet and theres a brook you make a Left and 250 feet up there it is Blue Eagle theres an Apartment complex built on the pool