As with other Greco-Roman myths, the connection is often through children, descendants or other family members. While Europa herself does not seem to have made it to the continental mainland, her brother Kadmos [Cadmus] did, and there, in memory of their hometown, he founded a Greek version of the hundred-gated Egyptian city of Thebes, although his rendition had only seven gates.
Kadmos' arrival on the mainland and his importation of the alphabet used by their people, the Tyrians and Sidonians, is significant because it only happens on account of his fervent search for his sister. It might be an intentional ironic twist that he never finds her (his sister, the Tyro-Sidonian princess) but he does find "her" (Europa, the continent). The mythology makes the effort to locate Kadmos not just in Greece but also further inland and northward in Illyria, where later misadventures end him up.
While Europa's eldest child Minos remained on Crete Island as its king, his daughter Phaidra [Phaedra] became queen of Athens, his brother Rhadamanthys became king of Okaleia in Boiotia [Boeotia] and his sister Alagonia moved to Peloponnesos [Peloponnesus] where the town of Alagonia in Lakedaimonia [Lacedaemonia] was named after her. The idea is, additionally, that the abducted princess Europa is the "mother" of these cities and their peoples.
There is a much less dramatic version, by the way, in which all the continents (or rather major regions) with which the Greeks were familiar—Europe, Africa and Anatolia—were named after daughters of the Titan Okeanos [Oceanus]: Europa, Libya and Asia respectively.1
1. According to Robert Fowler's Early Greek Mythography, the earliest attestation of this occurs in a fragment written by a certain Andron, who says that Europe & Thrace [or "Thraike," the region of warlike peoples to the NW of Greece] were Okeanos' daughters by an otherwise unknown Parthenope while the same Titan had another, even more obscure wife, named Pampholyge (or Pompholyge), who bore him Asia & Libya. John Tzetzes' commentary on Lycophron expounds upon Libya in this context.
Herodotus might be the only ancient mythographer to write explicitly about the Oceanid Asia giving her name to Europe's adjacent continent. Europa is an Oceanid in Hesiod's Theogony. This Oceanid, says Stephanus of Byzantium, bore Zeus a son called Dodon, after whom the city of Dodona, with its famous oracle, was named.