More an afternoon trip than a day trip, you can go to a riverside beach pretty easily. Buena Esperanza at the Rio Huancabamba is a good example of that. At the bus terminal on the main boulevard out of town (direction Chiclayo – Chachapoyas), you can either take a colectivo car (2.5 soles) or a combi minibus (2 soles) to Buena Esperanza.
Walk down to the river through the palm trees and rice fields, and try to find a spot with some shade. The water has an excellent temperature, but take care — the river is not deep, but it has serious force. The rocks are not sharp, but you will keep bumping into them, so bring water sandals. You can buy food at the football pitch, though it might be a better idea to bring your own picnic.
To get back to Jaén, return to the road and flag down a passing minibus or colectivo.