Came back to this. No phone number I could come up with, but here’s a variety of info. Your best bet for finding the phone number would be to request a copy of the 1969 or 1970 New York County White Pages - that’s the only sure documentation that might have it.
One of the things I’ve learned from NELSAPing is that most ads for, at the very least, skiing-related businesses (mountains, shops, etc) around that era simply did not list a phone number - not even an address, for that matter. Generally, the best you’d get is a hand drawn map, or directions saying something like “17 miles north of tunkabunket, new jersey off route 31A”.
Probably contributes to why it’s been difficult for you to track it down.
An old photo of the shop from 1973: https://quod.lib.umich.edu/u/ummu/x-06-08743/06_08743
A photo of the shop’s storefront from 1973: https://quod.lib.umich.edu/u/ummu/x-06-08742/06_08742
Two newspaper articles talking about the business: https://www.nyshistoricnewspapers.org/?a=q&hs=1&r=1&results=1&txq=%22Streeter+and+Quarles%22&dafdq=&dafmq=&dafyq=&datdq=&datmq=&datyq=&puq=&txf=txIN&ssnip=txt&ccq=&ctq=&e=-------en-20--1--txt-txIN-Streeter+and+Quarles---------
A 1970 ad for their Ottawa store: https://www.newspapers.com/article/the-ottawa-journal-leslie-streeter-co-ow/191337/
