What is the difference between vecchio and anziano? They both mean "old". Which one would you use to say a place is old, vecchio or anziano?
Actually, it depends.
Anziano is always inappropriate for places, unless we are under an allegory or some sort of personification, or any other figure of speech, however sophisticated.
If you are referring to the old bus stop, and there is a new one 100 meters ahead, you should say "la vecchia fermata", as opposed to the new one. For a crumbling building, you may say "quell'edificio è molto vecchio", even if I would prefer to use a more precise term, such as cadente, fatiscente, or pericolante.
But if you are talking about an old church, you should use antico or opt for a high-register term such as vetusto. "Una chiesa vecchia" is a poor word choice: either you want to say "la vecchia chiesa" (because there is a new one) or "una chiesa antica". If you say "Quella chiesa è molto vecchia" people may think you are pointing out that the church was built in the Seventies, and some handymen have to be hired because it needs some refurbishment. Well, that's really not the case.
Vecchio is a general term meaning old. When referring to an old man anziano is the term that is generally considered more respectful.
If you want to refer to a place vecchio is the term you should use. It has the same connotation as in English meaning both a place that is many years old and a place were you used to go, your old school!.
Vecchio - also means "Elder"; used to distinguish two important persons of the same family sharing the same name and surname. Example: Bruegel the Elder/Pliny the Elder/Cosimo dei Medici, il Vecchio - Cosimo dei Medici, the Elder - to distinguish this person from say another Cosimo of the Medici family who may be younger (in Italian Novello). Likewise could also mean an elder of a tribe or council elder (i.e an Alderman). Interestingly the Arab sheikh means old-man or elder. Plural of the Italian noun (and adjective) Vecchio is Vecchi (Elders, Old-men)