This district capital is a small isolated town, with a wonderful setting. At the back, there are forested mountains, in front you have a view of the big river valleys. The town itself is more charming than you would come to expect. Of course there isn't a whole lot to do, but locals will probably be happy to show you some of the wonders of the district.
Nearby is the village of Puentosillos. There is no road connecting these two places, but it's possible to walk the distance. That is, if you feel up to it: the sun burns and the slopes are pretty steep, and the path can get quite muddy. You might get someone to lend you a horse or mule. Close to Puentosillos there are some impressive things to see.
It is possible to do a daytrip from Jaén to Santa Rosa to Puentesillos and back, though it might be a bit rushy. Check the daytrips section in Jaén for more info.