day trips from Collioure

You may not want to leave Collioure as it is so special. I can’t help you with public transportaion as we had a rental car while staying in Collioure, one of our favorite coastal towns anywhere. You can head towards Ceret, or south to Costa Brava in Spain(Cadaques, Begur) and make sure you visit Figures,Spain and the incredible Dalí Museum, one of a kind! Perpignan is nearby, Carcassone a possibility and also Toulouse. You could also go into the Pyrenees but probably need a car.
Enjoy beautiful Collioure!

I based in Perpignan and used only public transportation. I was able to visit Collioure, so I know you can get to Perpignan. Once in Perpignan, the following places are accessible, but you'll need to check schedules to be sure the extra leg from Collioure to Perpignan doesn't make the trip too time-consuming for a single day.

• Yellow Train from Villefranche-de-Conflent to Latour de Carol (very high recommendation if you can make the timing work)
• Banyols
• Ceret

As far as the Yellow Train is concerned, it's more about the trip (through the Pyrenees) than the destination. Villefranche-de-Conflent is a picturesque but highly touristy fortified town. I didn't make it all the way to Latour de Carol myself; Bourg Madame or even Mont Louis would be a fine place to hop off the train and head back toward the coast.

While staying in Montpellier I was able to make day-trips to Sete and Narbonne. I believe they would also be viable from Collioure.

I, also, recommend Ceret. It was a hangout for such luminaries of modern art as Picasso, Braque, Gris, and Matisse. Many works by them and others are displayed in the Musee d’Art Moderne. A selection of works is also reproduced in tile at various outdoor spots in town. There is, in addition, a museum of Catalonian musical instruments, very worth visiting.

Montpellier, Sete, Narbonne and Carcassonne are all well worth a visit, and doable by train
BT

Of course, relevant answers to questions like yours really depend on what you're looking for.

We've stayed in Collioure 8 times and we're going again this year.

One thing you can do is walk to Port Vendres (the next town toward Spain), go to the market there (Saturday), and then have lunch, and after walking around the port just to see it, walking back. We've done this during most of our Collioure stays.
There is a series of very interesting historic photos of the harbor posted on the light poles which line the harbor.
(The day we were looking at these photos in a leisurely way we got pooped on by a seagull! Oh, what a mess! But it sure made for a great story afterwards!)

In 2016 we went for the first time to Elne. Took the train to, and the bus back (bus is only 1 euro) because it best fitted our schedule. Great street market on Friday. Got some wonderful fresh prunes there. The museum there is the Museé Terrus. Terrus interested us so we went. Then lunch at Au Remp'Arts, restaurant, 3 Place Colonel Roger. Lunch for us was superb. The creamiest goat cheese I've ever had. Plus, one of my favorite desserts is tiramisu, and their tiramisu was the best I'd ever had ever. And the setting of the restaurant is lovely. In good weather, which we had, you can eat on the terrace. The chef came out and walked around to the tables just to say hello. Very charming. We're going back this year for sure! You might want to make reservations.
Then after lunch we walked out to another and very special museum housed in a mansion which housed its subject, which is a maternity hospital founded by a Swiss nurse during World War II to give refuge to Spanish Civil War refugee women and especially pregnant women and their children. The nurse was a gutsy woman, and held off the Nazis for several years, also hiding Jewish women and children. Finally the Nazis shut the place down. There's a very moving filmed interview with the nurse as a older woman. N.B. If you're not into walking, best to take a taxi out there, because it's a longish walk, and along a narrow road. If you're a walker, it's definitely doable, but not necessarily pleasant. It's called La Maternité Suisse d'Elne at Chateau d'en Bardou, Route de Bages.

We also have taken day trips to Banyuls-sur-Mer, the next town toward Spain after Port Vendres. For that we took the train, but you can also take the bus. While there we walked (45 min.) out into the hills to visit the former home and studio of the great French sculptor, Aristide Maillol, many of whose sculptures are prominently featured in the Museé d'Orsay in Paris. Then, after walking back, lunch at the delightful La Vielle Cave. It's on a very quiet pedestrian-only side street. We ate outside under an awning. Very cozy. Had the 11 euro Formule, which included a 1/4 litre of wine per person. Good food, at an excellent price. If the weather is rainy you'd eat in their very charming and warm cave.

Someone else recommended Ceret. We've also went to Ceret. Good museum, and lovely town. But takes a lot longer to get there. We took the train to Perpignan, and then a bus from there to Ceret.