In New Orleans
New Orleans is not a place where surf the surf craze really took off. Finding material for this show isn't totally done online, but rather trawling through any pile of records I can find hoping for instrumentals. If you're hoping to dig in, I can make it easier for you. Keep in mind that this is *just* for surf instrumentals. If I were to list great record stores I would have a few more and in a different order.
My #1 recommendation is pretty surprising actually. It's Louisiana Music Factory. Despite the store's local focus, the guy in charge of their vinyl section is a surf nut. I found this out after knowing him for possibly even a decade (he used to work at Magic Bus records). While they don't have many originals, they always keep a healthy stock of reissues on Sundazed, Norton and even a few lesser-known reissue labels. Most will be in a section for surf/garage/etc.
Then I would check out Euclid Records. At the end of their rock section instrumentals actually have their own category. Some of them are ho-hum with some cheapo twistin' records and Ventures, but they also carry great comps like Strummin Mental. I believe they also stock Satan's Pilgrim's latest record. Euclid seems to be becoming the first place people go to for selling used vinyl, so they do get originals in from time to time, including 45s. You just have to stop by and see what they have!
Domino Sound Record Shack doesn't have their own instrumental section and the only surf artists you will reliably find are Dick Dale and Link Wray (Link Wray's not surf, yeah yeah). But they also tend to bring in interesting used stuff and their compilation section has some great surf selections (Surf Creature vol 3 was there last I looked). They're also big on their world section, so a lot of the interesting compilations I've bought like Shadow Music of Thailand and Bollywood Steel Guitar came from them.
Double Crown consistently puts out great music as a label with modern heavyweights like The Madeira, the Volcanics, The Tomorrowmen, the Surfites and more, but I've also been impressed by the stuff they've imported from Europe. They have pretty frequent sales as well
Deep Eddy Records is right next door in Texas. I've actually had the pleasure of meeting Ted, who runs it. Deep Eddy also has a great label lineup with groups like the Surf Zombies, The Nematoads, and Kill, Baby... Kill. Deep Eddy's real strength is the prices, where they tend to beat everybody out. They also carry Rondo Hatton's records, based out of Baton Rouge.
Get Hip isn't surf specific, but if there's something I just can't find an American store for, there's a chance that Get Hip will come to the rescue. I always try to take a glance every once in a while.