This place is great, located in Rochester NY.
The best shop I know of for Jazz is on 236 W. 26th St, between 7th and 8th Ave. It's called Jazz record center. They do have a website.... I hit it last month, and it was very impressive. It's on the 8th floor of a building, so you could walk right by it, without knowing its there. I also like Other Music in Noho. A couple of blocks down from Other Music is In Living Stereo, which have both vinyl and audio gear. On my recent trip, I also hit all 3 Academy record Stores. You may want to check out the Academy that specializes in classical, since that's what you are looking for. The only store that has more new than used, is Other Music. The Academy's, ILS, and Jazz Record Center are primarily used. The bopshop that Albert mentioned is long way from NYC, but looks very interesting. Thanks for the tip Albert. Just thought it was worth mentioning one last thing. There is a shop in Montreal called AUX 33 Tours. This is my favorite, and it is VERY well stocked with new vinyl. I generally go for used though.
Albert is correct about the Bop Shop, but Rochester is 5 hours North West of NYC (I live there). If you do ever make it up here, we have a ton of amazing record stores for a city of our size. For work, I travel to every major city in the U.S. for the past 15 years and I've never seen half the amount of vinyl shops that we have, even in very large cities. We have one place called The Record Archive that's so big they put in a stage and have live concerts right in the store. I went there on a Sunday morning a couple of months ago and the parking lot was packed. I couldn't figure it out until we got inside that there was a band playing to a huge crowd of people in their early 60's rocking out with cups of coffee in their hands. Who books a gig on a Sunday morning?
I thought it was closer than that, but fortunately the Bop Shop has a great on line presence.
To their credit, every Item I've received was exactly as graded and Bop Shop frequently stocks hard to find Jazz titles I could not find locally.
I used to drive to Princeton back in the day for vinyl. Now i just buy online. Interestingly, I've have had fewer problems with used records on places like e-bay than I have had buying reissues from the usual online sources- lot's of crappy re-repressings- no fill, stitching, etc. Today, got a brand new copy of a record from one of the usual online sources and the cover was bent. I'm not going to send it back, because I bought it to listen to, not as a collector's item. But, even when paying for new stuff and often expensive 'audiophile' vinyl from established suppliers online, it's iffy. Real record stores are great. I wish there were more. I haven't gone record shopping in Manhattan in years, but used to haunt all of them.