I have a couple of articles that State run museums are free to people of 65
Over 18 / under 65? Pretend you're Canadian
For arcane political reasons, most national and state-run museums in Italy (any place with an official title that includes Museo Statale or Museo Nazionale) are either free or offer reduced admission to anyone under 18 or over 60 or 65...WITH THE EXCEPTION OF AMERICANS. No, this is not anti-Americanism run amok. There's a perfectly good explanation. (Warning: arcane political reason coming up.)
These museums and sights are free to both the callow and the distinguished is because the governments of most countries have signed a reciprocity agreement to grant one another's youths and seniors the same discounts they would get at home. The United States never signed this agreement since there are no national museums—or rather, there is only one, the Smithsonian, and it's already free. (OK, so it's not a explanation we get to be happy about, but it is a legit one.)
That said, many ticket-takers at individual sights could care less which country issued your passport. They understand that, no matter what the nationality, students are poor and seniors are often working on a tight budget, so they don't bother enforcing the anti-Yankee provision—sort of a don't ask/don't tell policy.