First things first: If you need a place to stay, check out La Casa de Rafa (also called El Numero 8). Innkeeper Rafael is awesome, and very knowledgeable about Granada. He actually meets you a few streets away before you check in (it's very hard to find the place if you don't know where you're going!), and on the way to the hotel he shows you a few local restaurants.
One restaurant, Mesón del Trillo (Callejón del Algibe de Trillo, 3) serves up a wonderful array of delicious cuisine. For starters, their bread is clearly NOT frozen, and before you can decide what you'd like to eat, they place an apertif in front of you (our server told me they take one of their dishes and make a puréed version since they don't offer soups on the menu). The one we had included fava beans (habas en Español) and was very tasty. For an app, try the tomato salad.
Between the salad and our main dishes, we were presented with a second tiny glass, this time a palate-cleansing shot of pineapple sorbet.
For the main dishes, try the pork medallions with mustard sauce, or their delicious house-specialty rice dish (it includes artichokes, fava beans and small clams).
For dessert, try the cheesecake, the blackberry "cake" or the bizcocho de avellana con chocolate caliente.
This very well may have been the best meal I have ever eaten, and the servers are well-deserving of a 15% tip (VERY generous, judging that it is common to not give tips at all). Also, the local Granada wine on the menu adds yet another enjoyable facet to the meal. I highly recommend this establishment.
If you are not in the mood for going out and you want to cook in your own kitchen (or the one in your aparthotel), check out the Mercado Central. There is an abundance of fresh fruits and veggies, seafoods, meats and cheeses.
There are also a number of fruterías scattered around the city, and I even stumbled across a spice/tea market.
As far as tapas go, you really do get them for free in Granada. With the order of any alcoholic beverage (try the tinto de verano -- vino tinto + Fanta limón) or refresco, you can expect a selection of tapas. We visited one bar and received small ham & cheese sandwiches on bagel-type bread, a heap of tuna & pasta salad, and tater chips with a ketchup-like sauce and creamy dip. Of course, you can always go to a bar and order raciones (plates) of tapas, but you'll have to pay for them, and there's only one rule: They have to be tasty.