Spain has put efforts the past decades to secure and prevent it´s most beautiful and sensitive areas and established quite a number of national parks.
The closest one is Parque Natural de las Sierras Subbéticas 1 hr drive from La Fe. Located NW.
South of the park, the lake Iznájar, which can offer a refreshing swim.
Quite a number of restaurants are located in the village Iznájar.
The selection is huge and several parks can be visited by car.
One road f.x. leads west from Montefrio (GR-3410), follow this and then take left (south) on (A-4154) in direction Loja. Many beautiful places for stop by are found along the road A-4154.