YES, YES, YES!!!!! Especially if you love landscapes, adventuring forth into the province is definitely one of the things that I would recommend most highly to those who are able. Even if you aren’t interested in seeing beautiful landscapes but you have underestimated the Andalucian heat, an escape to the countryside (especially to a few specific spots) is exactly what the locals recommend.
The Sierra Nevada Mountains is one of these areas. The several mountains rise over 3,000 metres (11,000 feet), so you can literally climb to escape the heat. When I climbed along some of the peaks (such as the two highest, Mulhacén and Veleta, in August 2017), the temperature for most of the province was around 38°C (100°F) whereas the mountains were around 10°C (50°F). Definitely worth the escape there! And the sights were beautiful. On clear days you can see for many kilometres. This does depend on the dust coming up from the Sahara though. It can be quite difficult to recognise anything due to the general haze in the atmosphere.
If climbing mountains really aren’t your style, the base and foothills also offer both relief from the heat and shade. Many of the rivers have cut small valleys where larger vegetation flourishes and they grow closer together. Inside these valleys, the temperatures are often 10°C (~ 19°F) lower than the surrounding areas. You can also bathe in the water which comes from the mountains (i.e. it is freezing!), although on very hot days, you should be at the pools somewhat early as it is assured that many people will have similar thoughts!
Another place to escape to is the beach, which is about a 45-minute drive from the capital.
Here are some more images: