If you wish to spend your vacation in complete comfort (A/C and heating both work extremely well!), just a minute or two by foot from several good restaurants, cafés, bars, and historic monuments, you will be very happy in "La Brigade". Moreover, Narbonne is well situated to take off for one of the two beautiful Mediterranean beaches, bicycle along the canal, or to explore "Cathar country".
The apartment is only 10-12 minutes by foot from the Gare (train station) de Narbonne, from where a short train ride will take you to Montpellier, Sète, Agde and Beziers to the North, Carcassonne and Toulouse to the West, and Perpignan and Collioure to the South.
Now that the Spanish AVE trains are in service, it's even possible to do Barcelona as a day trip... although it's such a fabulous city that I would recommend spending two nights there minimum!