Proctor and West Rutland were where some of the bigger marble quarries were. They’re still very much so accessible in West Rutland. I grew up there and spent considerable time there playing around the quarries as a kid.

Feel free to DM me with any questions. It’s not near Burlington though. No marble quarries are as far as I know, it’s more slate as your get closer to there. Proctor and West Rutland are about 2 hours south of Burlington in the central-south portion of the state

https://www.google.com/maps/place/700+Marble+St,+West+Rutland,+VT+05777/@43.6051977,-73.0533338,16z/data=!4m6!3m5!1s0x89e022efc492dd2b:0x7cf2f1a4a4aaed1b!8m2!3d43.6067944!4d-73.0542646!16s%2Fg%2F11tfkr87g0