Agde Day Trips
Toulouse-Lautrec Museum
We went to Albi as well; the Toulouse-Lautrec museum is amazing for fans of his work, and the drive there (through the vineyards and mountains) is breathtaking. The museum is definitely worth the effort and it can make for a great day away from the resort.
Carcassonne, Marseilles, Sete and Agde
Carcassonne is very popular with the tourists. While something to marvel at, it will be crowded, especially during the summer. (Cascassonne is generally on the way to Albi). Marseilles is doable as an all-day trip, but you won't have enough time to see everything. The nearby towns of Sete and Beziers are cute. Sete, especially, is very charming. Agde is surrounded by vineyards that make some of the best wine in the world. It is really worth your while to go exploring, stop at some cafe, order the house wine, and see how good and cheap it is.

Albi and Montpellier
During my stays there have been windy cloudy cool days - a group of us went to Albi - about 2 hours drive with stops in St Chinon [vineyards] - really interesting as a Cathar centre and also the birthplace of Toulouse Lautrec; and another time [day trip] to Carcassonne - amazing hilltop fortified city. Montpellier is also adorable and only 60km away.
Avignon, Camargu and the Rhone Delta
Avignon is another place certainly worth considering during a stay at the Cap, with the place being a very nice city with a medieval city centre nested within old city walls. Don't recall how long it took driving there, but you can do it on a day trip. There is also the Camargue, the Rhone delta, if you like nature.
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