I visited during the summer of 2012 with my teenage son. Food options up on the Alhambra are not great. The Parador really is your best bet. Inside, you'll find a casual lounge where snacks (tapas, sandwiches, ice cream, dessert, drinks) are served. These are very tasty and reasonably priced, considering you're in an upscale hotel.
The restaurant is just in front of the lounge and it offers a wonderful Menu del Dia (set lunch or dinner). Dinner was 34 euros and we sat outdoors in the garden, facing the Generalife Gardens. Granada is not a cheap place to eat; I guess they get a lot of tourist business. Across the valley in the restaurants of the Albaicin, we had a similar meal for 75 euros!
In the visitors' centres, there are vending machines with sandwiches and drinks. It is ... vending machine food, lol.
In the little gift shops, they sell a few snacks but nothing too substantial.
The other option is eating in the patio of Hotel America. It's a cute hotel next to the Parador. DO NOT EAT HERE. It looks quaint and you think it'll be cheaper than the Parador. It's a huge rip-off. I stayed here one night and had to pay 8 euros for b'fast the next morning. I should have taken a picture of the food. It was so outrageously bad.
If you have time to ride the Segway in Albaicin, do it! It's a great way to see the area and a lot of fun too.
Edited: 2:11 pm, January 18, 2013