Avignon has two train stations: “Avignon Centre,” within walking distance of the Palais des Papes and “Avignon TGV,” which is 5 km outside town and has regular train connections (about twice per hour; 5-min ride) to “Avignon Centre”.
Taxis from "Avignon TGV" to the city center cost roughly 25€
The main airports serving Avignon are:
Lyon Saint Exupery (LYS) with TGV to Avignon, either directly from “Lyon Saint Exupery” (6 trains per day; 50 – 90 min journey; latest depature from LYS at 19:43) or via “Lyon Part Dieu” (roughly every hour; 30-min ride; Rhonexpress + 60 – 80 min TGV)
Maps of (left) Avignon center and (right) Avignon TGV: