Ile de Re, I suppose, though I don't know what it's like in April. You'd certainly want to pick a (comparatively) nice day. In high season there's good bus service over the bridge; I don't know about April. Ile de Re is a pleasant place, but I found it less interesting than other islands I've visited that have more variation of terrain. (I'm not a beach-goer, but then no one without a wetsuit would go in the water there in April.)
I though the town of Saintes was a worthwhile side-trip (over an hour by train), but I like picking places with nice historic architecture and just wandering around.
Poitiers is farther, requiring over 90 minutes by train. It's an historic city with some very old churches and a very pretty, hilltop historic area. Nary a foreign tourist is sight during my late-June 2019 visit.
I think La Rochelle is primarily a beach resort. It has a nice feel to it; it seems to get overwhelmingly French visitors. I'm not sure it's long on traditional sightseeing, though I enjoyed quite a few hours just walking around.
Food:
As of 2019 La Rochelle had a chocolate-macaron shop (called, fittingly, Cacao et Macaron). I can't remember whether I ever got around to trying the macarons, but the artisan chocolates were good. Not cheap, but they didn't seem to be overpriced because of the location in a beach resort. Just normal $$$ pricing for artisan chocolates or a bit less.
I also enjoyed a meal at La Salle a Manger in La Rochelle. Limited menu, nice food, not overpriced. (I'm not an expert on food, but I like interesting flavors rather than eating the same thing all the time.) I tried to go back for a second meal, but it was the day they were closed. https://www.lasallamanger.fr/la-carte