The Romans knew where Troy was, it was still inhabited during the Classical Period. Settlement at Troy does not stop with the destruction of Troy VIIa. Settlement continued through the Archaic Period (during which time an important cult center of Athena was founded at the site) and the site was still inhabited in the Roman period. The site of Troy became a rather popular tourist center during the Classical Period, and especially so under the Romans, under whose patronage the city did pretty well. Our authors are, however, not without their doubts that the site was genuine. The contemporary site of Troy was essentially a collection of supposed heroic sites and shrines built up around the Archaic temple of Athena, and the inhabitants tried to pass off as much as they could as of genuine Homeric vintage. Educated people who were willing to stop for a moment and think about it don't seem to have necessarily bought it, although there were many who didn't care, and there were so many Homeric relics floating around the Mediterranean that the claim was not quite as fanciful as it seems in hindsight. There were competing sites for the Homeric city, and thought the site that was built up (and that we know was the actual site of Troy VIIa) more or less won out it was debated whether these alternate sites were in fact the correct ones--Strabo, for example, argues (erroneously) that the Troy of his time is a fake built much later (which I mean...yeah...on top of--really next to--the old site) and that the real site of Homeric Troy was a little village in the foothills of Ida