Tickets in Provence are small money and transport is not: the moment you need a hire car for the Luberon your daily spend roughly doubles, so the whole budget question is how long you can avoid one.
HI Avignon hostel
17 rue de la République, inside the walls and a few minutes' walk from the station: 65 beds in rooms of three to ten, with a bar, a snack bar and luggage storage, open year round. Check-in is 4pm to 10pm and there is no bike garage.
Camping and Auberge Bagatelle
On the Île de la Barthelasse facing the Pont d'Avignon: 141 beds, mostly dorms of four to eight, alongside tent pitches, a bar and two restaurants. Cheapest sleep in Avignon, at the cost of crossing the river every time you go into town.
Use the ZOU! network instead of a car
The regional buses and trains reach Carpentras, Cavaillon, Arles and Nîmes from Avignon and cover most of what you would otherwise drive to. The Carte ZOU! Malin costs €20 for a year and takes 30% off every fare; anyone aged 3 to 25 can buy the Pass ZOU! Études for €45–90 and travel unlimited for a year.
Musée du Petit Palais, free
The permanent collection of medieval and early Renaissance painting costs nothing, Tuesday to Sunday, closed Mondays. It is the obvious wet-afternoon move on a day when the €16 papal palace ticket is not happening.
What a day costs
Admissions are cheap: Village des Bories €8 and free under 12, a guided walk at the Colorado Provençal €9 for adults and €4 for a child of 6 to 12, the Sentier des Ocres €3.50, the Petit Palais nothing. Parking at the Pont du Gard is €9 per vehicle however long you stay, and a hire car plus fuel will comfortably outspend every ticket you buy in a week.