Would travelers suggests staying in Avignon old town or in one of the smaller quainter areas near Avignon?
I prefer to stay in a village or smaller town in Provence, especially if I have a rental car. Avignon is a bear to drive in.
I stayed at Hotel du Parc, not far from the central train station in Avignon recently. There are two other hotels on that same quiet street--check the RS book on Provence. Avignon is small enough to be walkable; I recommend staying inside the city wall.
I'd go with smaller city like Arles or Nimes, or with car in a smaller town, which are many.
That's based on day trips to Avignon as I've never actually stayed there. But that's my opinion.
I was an exchange student in Avignon in fall 2004 and loved it... however, I know nothing about hotel accommodations there as I stayed in a dorm.
I just wanted to post to reinforce what another poster said: do NOT go outside the walls at night. Since I assume that you'll want to walk around the city at night, please get a hotel the city center (or at least inside the walls). I've heard many a story of people getting robbed (or other crimes) happening outside of the walls!