Well, we just don’t know. Apparently she must have stuck around for Pentecost, and she probably hung around doing the same stuff everybody else did in the early early Church.
There was a fairly substantial Christian population in Roman Gaul (today’s France), and there are various legends of who founded it. Mary Magdalene and Martha and Lazarus show up pretty late as legends, but anything is possible.
The older Eastern and Western tradition is that Mary Magdalene did go around various places with the Apostles, evangelizing along with them. (Not difficult to believe.) She had, after all, evangelized the Apostles about what she had seen in the garden.
A specifically Eastern/Eastern European tradition identifies her with the first Easter egg. She allegedly was witnessing to the Emperor in Rome about Christ’s resurrection, when he said that it was more likely that the egg in his hand would turn red, than a man should rise from the dead. So it did.
There’s a substantial body of legend out there for all sorts of things about her, though. Like most of the early Christians mentioned in the Gospels. And like most of them, we don’t have much definite information. That’s just the way it goes.