To add: much will depend if you'll have car access.
The old tow of Ceret, for instance, is lovely (great modern art museum too, with stacks of stuff).
And there are also loads of really little villages all the way down from there to the coast. No train access up there, but buses occasionally.
The buses are €1 and air conditioned and very comfortable, but they are few and far between for the really outlying villages.
There is also Salses – which is accessible by train (it's a couple of stops before Perpignan). It has a fabulous old fort to look around but, for a longer stay, there's an etang nearby with water sports etc. I think it has camping and other accommodation.
However, I really cannot recommend the Languedoc-Roussillon enough. And even slightly outside: if you fancy the mountains, there's Foix (via Toulouse in terms of rail travel), which is lovely (we even saw a European vulture flying above).
I would also always recommend Villefranche de Conflent, which is a remarkable walled village (far better, in oh so many ways, than Carcassonne) and with a walled fort on the hillside above. There are 4x4 trips to Fort Liberia, plus helicopter trips to the top of nearby Canigou, which is the sacred Catalan mountain. Oh: and some grottos.
Very nice Dutch-run B&B just below the station (with swimming pool) and one super restaurant in the village itself.
We did Foix to Villefranche de Conflent in one day, by train, via Latour-de-Carol, on the famous Yellow Train. I'd tend to avoid that: it's very long and very bumpy. But you can get a train from Perpignan to Villefranche de Conflent easily.
There are so many gems like that.
