If you want alternate history, first we have to agree what the Trojan War really was. That he was not exactly as described by Homer is certain, after all. Even if you cut out all corporeal interventions by Olympic deities.
I find it plausible that the TW conserves knowledge about the Bronze Age collapse of 1200 to 1150 BCE. One radical possibility would be that a strong city-state survives and maintains control of the Dardanelles. Therefore the Phrygians are unable to leave their homeland in the Balkans or enter Asia Minor in much lesser numbers. So they are not in the right place to finish off the Hittite Empire, which might have been an ally of Troy/Ilios/Wilusa anyway. A larger Hittite Kingdom in place of some Neo-Hittite statelets would be a *huge* change to pretty much all of history.
Alternatively, it might be interesting to compose a TL based on Hellenic traditions: Odysseus is killed, so the other Achaeans return in disgrace. Since the temples of Troy have not been desecrated, the wrath of the god does not hit them and most survive the return to their loving spouses. The survival of the Mycenaean elite has wide repercussions in the following years and decades when the Heracleids try to claim their ancestral lands of the Peloponnesos. Oh, and in this TL (depending if you see Virgil as canon) there will be a Pallantium, but no Lavinium and thus no Rome as we know it: No Aenaeas in Latium, no Romulus and Remus.