We love to hike as an antidote to time in big cities. We would love to take a day hike in the Sierra Nevada. We will be there in October and will have a car. The most important thing is a big view. We are fit but not climbers. And a recommendation of where to stay as well. Happy trails!
I am not so sure about hiking options BUT if you have a car and really want to explore the Sierra Nevada, you could head to the Alpujarra Granadina area. The villages like Sotorpújar, Pampaneira, Capileira, Trevélez are really pretty, and some of them have very good mountain views.
They're at the foot of the mountains, and Trevélez is already at 1,500m a.s.l., so hiking opportunities are definitely plentiful - I just do not happen to know the specifics.
There could also be some good hiking opportunities closer to Granada, between there and the Sierra Nevada ski resort (which you should avoid, ski resorts in summer are mostly eyesores), above Monachil for example. But that's just a hypothesis!
If you go to AllTrails and put in a place, you will get many hiking trails with all you need to know.
I typed in Allpujarra and it gave me 196 trails. Allpujarra is a general term, but you can narrow that with a new search if you put a more specific place name. Like Granada. Or even more obscure towns.