Valerie, I agree with visiting Mirepoix, a lovely town. You are also not far from Lagrasse, one of the Plus Beaux Villages of France.
Are you familiar with the history of the Cathars? I didn't know about them before we first went to the Languedoc several years ago, and it's a fascinating although rather sad episode from the Middle Ages. You are more or less in Cathar country there, and there are a lot of ruined castles in the area. Peyreperteuse is very dramatic, but it may be a little farther than you want to drive (I think it would be about 1.5 hours).
Here's a website about the Cathar castles, and
here is a page from a trip report I wrote on Slow Trav about visiting the area, when we stayed south of Carcassonne.
We also have stayed in Marseillan on the Languedoc coast. I think that would be about an hour away from where you're staying. We were there in late October, after all the beachgoers had gone. I imagine it would be very different in summer, probably packed with crowds. If you like oysters, that is prime oyster country.
Here is a photo album from that trip. You might find some interesting destinations among those photos. For example, the Abbey of Valmagne is a beautiful place, now desanctified and a winery. They store wine barrels in the arches in the church. I also enjoyed our visit to the Fontfroide Abbey.
The Noilly Prat vermouth factory in Marseillan was a very interesting tour.