You will want to send postcards right away to Mom and Pop and friends, right? You can buy the postcards anywhere and usually tobacco shops will have stamps, too, to avoid lines at the post office. Just say, “Posso avere un francobollo per (your country)?” Ask for prioritaria (airmail).
Drop these in any red postbox on the side that reads altre destinazioni, destinations other than Perugia. If you need a letter weighed, go to a Tabaccaio or the main post office on Piazza Matteotti (see Post office in Perugia a-z). Go in the main room and press the button on the yellow machine under, “spedizione e ritiro lettere e pacchi,” then wait your turn.