The most rewarding activity around Santa Rosa is the walk to the nearby village of Puentosillos. There is no road connecting the two places, so foot or mule is the only option — and that is part of what makes it interesting. The path climbs steeply through forested hillside, with the sun bearing down and the slopes getting muddy after rain. It is not a casual stroll, but if you are prepared for a genuine hike it is worthwhile.
Locals may be able to arrange a horse or mule for the journey if the uphill sections are too much. Ask at the town square and someone will usually know who has animals available. Near Puentosillos there are several things worth seeing — a waterfall, impressive rock formations, and views back over the valley.
The round trip from Santa Rosa to Puentosillos and back is feasible as a full day from Jaén, though it is tight. It is more relaxed if you allow yourself a night in Santa Rosa.