Based on Rick Steves great recommendation, I had the pleasure of staying at Aux Augustins in Avignon. It was exactly as Steves described - a beautifully appointed room with great French flair, immaculate, well located in an area of the city that is a 10 minute walk from the tourist attractions. All of the rooms overlook a lovely walled-in garden with rambling roses and other fragrant flowers. As this is a self catering venue, the garden served as the perfect place for me to enjoy a leisurely, and inexpensive, breakfast before setting out to see Avignon. Across the street from the hotel is the local open air market. I particularly liked staying in an area of town that was filled with friendly locals rather than a "tourist hotel".
I would recommend Aux Augustins for singles or couples. Additionally, I suggest booking directly with Aux Augustins. The wonderful hosts Sabine and Patrick offer special rates for Americans.
Staying at Aux Augustins helped to make my wonderful stay in Avignon perfect.