From the front at Palamos you can walk along the promenade all the way to Cap de Roques Planes and back. As a daily morning constitutional it'll keep you out of trouble.
The afternoon can be spent idling on the beach and the evening is too short, with the shops closing at 8pm, aperitifs to be drunk, tapas to be tried, supper de be decided and the mandatory promenade around the port looking at the fishing boats as the sun goes down.
Another popular bike ride, somewhat longer and steeper, is up to Romanyà de la Selva.
The next little bay north of Palamos is La Fosca, very pretty, though the walk isn't, unfortunately, though it doesn't take long. However, from La Fosca the walk of less than an hour to the beach at Castell, more than makes up for it, with Iberian settlements to boot.