I remember there was a used vinyl record store in Nakano, maybe it's still there. Nakano is a 5 or 6 minute ride from Shinjuku station on the JR Chuo Line (orange, first stop) or the JR Sobu Line (yellow, third stop). Take the North exit from Nakano station and walk on the main cross street towards Sun Plaza, the tall building a short distance away. If the store still exists, it's on the opposite side of the street from Sun Plaza, the side you are on, and before you reach Sun Plaza.

An alternative more "advanced" way to get there is to exit the Park Hyatt, turn left at the bottom of the driveway and walk past the firestation, cross the street, and continue on about 150 yards to the first bus stop -- if you reach the grocery store, you've gone too far. Take bus route 45 (not 41) to the end of the line at Nakano station, costing Y200, and walk under the tracks towards Sun Plaza.