phild, hello, for CDs try the JECKLIN store at Heimplatz on Rämistrasse, but I must warn you, prices are attrocious, quite a bit more expensive than in in the States. Finding good vinyl is difficult. I suggest you try ANTIQUARIAT JETZER, at Seefeldstr. 189, he has a lot of classical, but also some of the stuff you are after. Prices vay from 10 to 50 Swissfrancs per LP. Basel, I don't know.
Happy hunting.....but don't expect to find LP rarities. The city abounds with cognoscienti! You'd have better chances on ebay. But then , one never knows, does one!