I've only spent 3 days in Granada a few years ago and came away with the same impression as Erica. The city is pleasant to stroll around and has the Alhambra, a must visit. On Calle Navas, beside Dos Diamantes, we like Bar Casa Jose for tapas and Fogon de Galicia for good seafood, mostly serve in racion sizes. Antiqua Bodega Castaneda just off the Plaza Nueva is good. There are pleasant outdoor eating places on the Plaza de Bib Rambla, good for coffee and drinks. The food is more of an after thought. Pasteleria Lopez Mezquita on calle Reyes Catolico is a very good traditional pastry shop/cafe. We really enjoy sitting there late afternoon watching the local scene. Like most businesses in Granada, it is closed between 3(?) to 5 pm in the afternoon.
Five days in Granada is a lot of time. If your traveling plans are not set, consider Seville as a base. It is a wonderful and lively mid size city, full of sites and eating places, great for just for walking around. Day trips to other towns including Granada, Cordoba are easy by buses or trains. A car in Seville or Granada is basically useless as driving and parking central is a big big hassle.
If you are game to go somewhere further out of town you can take the bus or taxi to Bar FM near the bus station - incredible seafood. Try the fried salmonetes (red mullet?) and grilled chopitos. Everything else is universally good as too - I wish I tried more! Don't expect it to be cheap though - fresh seafood costs money, even if the location is way out of town.
I was in Granada last year and had a wonderful time.
We stayed in the Albaicin.
Here is a thread I found useful.
I liked Diamantes (Seafood) near Plaza Nueva, Bodegas Castaneda, Real Asador De Castilla (Steak, Roast Baby Pig), Bodegas La Mancha (Bocadillos de Cochonillo) to name a few. Check out the little plaza San Miguel De Baijo in the Albaicin. It was one of my favorite places.
A couple of good places to explore for tapas are Calle San Matias and Calle Escudo del Carmen.
I was not swept away by the restaurants we tried in Granada, but things may have changes in the two years since. We had much better luck elsewhere in the region.
You are sure to receive more recent comments, but one place I would try for Andaluz fried fish is Los Diamantes, with two locations on Calle Navas, which has a bustling tapas scene. I might try to arrive when they open to avoid the heaving masses that will pour in later.
We also liked Restaurant Puerta del Carmen, in the same general downtown area, and Cunini,
Probably the best taste I put in my mouth during our days in the city was the Pastel Moruna from Lopez Mesquita bakery.
You can eat it there or take away. Not to be missed, it is a variation on the Moroccan bisteeya and, like many local dishes, a reminder of the Moorish history of the area.