Advice on reasonable rates and safe place to park within walking distance of Alhambra?
Walking up to the Alhambra is UPHILL. There are plenty of buses that will take you directly to the entrance and back into the center of town for less than 2 Euros. There is a parking lot, I don't know if you have to pay to park, but it is still downhill from the location. It's easiest with public transportation.
One tip: If you have prepaid for your tickets, walk past the ticket booths (on your left), straight back to the ATM-like machines on the right. Make sure you have the credit card you paid with, and print your tickets there.
It's beautiful, have fun!