There are several great towns not far from Carcassonne. The advantage of Avignon is you pass the Pont Du Gard on the way
France
Summer in the South of France- a Visit to Carcassonne
It probably wasn’t the best idea to spend a week in Carcassonne with a broken arm especially in a heatwave. The travel insurance would have paid up but sitting at home unable to do most things, try washing up or ironing with one hand, was driving me crazy so we went anyway.