Is a car rental necessary for Granada/Andalusia?

My fiancee and I have our honeymoon booked to visit Granada in a couple weeks (already have Alhambra tickets). We've got a pretty loose itinerary with a lot of flexibility for 10 days. I'm wondering how public transportation is for getting around the region. Should we consider renting a car for any short day trips out of the city, or are things relatively accessible via bus/transit?