A second vote for Le Plaza-La Paillotte near the Foundation. Had a fun. funky lunch at L'Aire d'Arles squeezed in on the ledge behind the theater at 25 Rue Prte de Laure. It has an art space upstairs and rotating art decorating the open restaurant. L' ÉCHOPPE by the city gates is a fun locals beer bar - with light food - if you want one. Heard good things about L O à la bouche also near the city gate but didn't get there. The Foundation is interesting depending on the exhibit. We were lucky and it was really interesting artist while we were there last year. With 4 days in Arles you'll have most of the old city mapped out in your head and probably feel like you're starting to belong there.
St Remy is my favorite little town in the region. It is charming, has an amazing market day and is close to both Van Gogh Asylum and ruins at Glanum right next to it. SR accessible by bus from Arles - about 45 minutes and the 707 bus passes Les Beaux on the way there and on the way back so you can do Les Baux as well if you want a really long but interesting day.
Nimes is a larger city but also an interesting day trip but train, but look for the direct trains and many go through Avignon. And Avignon is also a day trip possibility and easy by train.
Do try and do a Provencial market day somewhere as it is quite the event.
Have a great trip,
=Tod