There seem to be two threads here, about the first 76 golf clubs in the US, and also which of those are still playing golf on the same property as they were founded? Not sure anyone is keeping score on the latter, but it’s an interesting question.
At Brooklawn, founded in 1895 with golf, tennis, bowling, baseball, archery, shooting and a casino, they are still playing golf in the same spot. The original 9 hole course was on land currently occupied by the 11th thru 16th holes, plus a bit of the current first hole. There are two spots where you can actually see parts of that 9: on the current 11th hole, there exists the original 1895 tee for their 4th hole, and also on today’s 11th hole, you can see the original 5th convex green shape off in the rough. We still have no idea who was part of laying out the course, we just say it was “members”. Notably the first “pro and greenskeeper” was George Morris’s grandson Tom, but we have no idea if he helped lay it out.
The course was expanded in 1911 to 18 holes. Again, we aren’t sure by who, but the Pro at the time was George Sparling, who arrived in 1908. Tillinghast was hired in 1929 to build what is there today.