There are a few consignment shops that might have a few records (there is on on 23rd street between 6th and 8th if I recall correctly) … But there are no stores which have anything in real quantity, as far as I know.
I have not really noticed many vinyl records at all in Cuba.
But I checked on the Cuban classified site Revolico.com and there were two ads selling some vinyl records…
My best advice would be to contact these guys when you are in Cuba and see what they say. Chances are good that these guys know other people who have records too. There is a network for everything in Cuba.