The following are only a few suggestions and if you visit the house in Tarascon you will find many more suggestions left by previous visitors.
FOIX - a market town with Cathar castle (15mins by car or train)
AX-LES-THERMES - a spa town with casino with cable cars to ski runs in winter and hill walks in the summer. (30 mins by car or train)
USSAT-LES-BAINS - a small spa town with canoe rental etc. on the river Ariège. (15 mins by car or train).
ANDORRA - Duty free zone in the Pyrenees, (40-50 minutes by car or train -avoid weekends in the French Holiday season!)
MIREPOIX - Mediaeval town with magnificent square with mediaeval buildings. Many festivals and events. (30-40 minutes by car).
NIAUX - probably the finest cave paintings and a museum of rural life (10-15 minutes by car)
PLATEAU d’ABEILLE - beautiful walking area - often used in the Tour de France for the mountain sections ( 30-40 minutes by car.)