Ancient Greeks (under Roman domination) reached even up to China, as there are accounts of Imperial Roma sending over emissaries to the Chinese (Later Han) via sea. Indonesia too. A sailor of Massalia, under what some historians believe Megas' Alexandros command, sailed around Spain to England (Kassiterides Nesoi) "Tin islands" and even up to Norway (Thoule). Those are the limits of them that we know of. There are some suggestions that Ptolemaioi, after founding 3-4 colonies in present day Somalia, that they sent some ships down Africa, even up to present day S. Africa, but that is unconfirmed. It is MUCH MORE possible though than an actuall ship of Hellenistic times sailing to America.

Ancient Greeks reaching America? I honestly don't think so. Phoenicians maybe, even if that is VERY doubtful but Ancient Greeks NO.