Presuming the original legend of a Spanish bishop taking Visigothic refugees across the Atlantic Ocean cirva 711 AD was true and said cities survived, what might their culture look like by the time Columbus arrived?
Probably greet Columbus with the words "Oh, boyo, what took ye so long to find us?"
The culture would presumably be enmeshed with the culture that was present when they arrived (if there was any where they got to). Do you have any suggestions as to where they'd make landfall (Cape Verde, Brasil, Caribbean, Florida, Canada etc - Atlantic's a big place). Otherwise, the culture that they brought with them might be adapted to the current situation, seven centuries without any contact to the motherland is a
long time to assume that they'd keep a solely Visigoth culture.
But I'd definitely be interested in reading a TL where this is the POD