We will be in Madrid on business for 4 days and then down to southern Spain for 3 nights before heading back to Madrid to catch our flight home (no open jaw unfortunately); We planned to take the train or fly Madrid- Granada- Madrid but can rearrange the return to Madrid via another city. We wondered if using Granada as a base for the three nights is a good idea if we rent a car? Or, we can spend 1 night in Granada and leave late the next day (have 2 pm Alhambra tickets)and spend the remaining two nights someplace else.

I suggest you a trip to Baeza and Úbeda, two monumental towns at less than 2 hours from Granada. Nice tapas bars and restaurants. I like:
-Restaurante Museo Agrícola (Úbeda), dishes: pipirrana, lomo de orza.
-Restaurante Juanito (Baeza), dishes: escabeche de perdiz, choto frito.

I forgot it!
Check out:
www.geneura.ugr.es/ubeda.html

Revulgo, the link doesn't seem to work.
Could you post the path?

Try
http://geneura.ugr.es/ubeda.html

Before reading Revulgo 's post, I was going to recomend exactly the same Ubeda and Baeza. They are near Granada and both cities (10 minutes apart are fascinating. We stayed in the Parador en Ubeda, but I was thinking of staying in one of the nice small hotels in Baeza. If you choose the Parador, it is located in the old palace of a Bishop, it is very nice, however be sure they give you a nice room, some are interior rooms which are not nice. The food there is very good.
Both cities offer walking tours which are very interesting, inexpensive and fun. I took them in Spanish though I do not know if there are tours in English.
I do hope you follow Revulgo 's idea, if so I envy you...

Also Cordoba is very interesting!

Though Ubeda/Baeza is a good trip, 1hr40min away, another choice is Priego de Córdoba, only one town, 1hr20min away, smaller, with different sceneries and a good restaurant. Take a look at http://www.turismodepriego.com/ and come back for details if intetrested.

Thank you Josele for pointing out Priego de Cordoba which looks as a wonderful place to visit and stay getting out of the beaten path.
I thought that without a car I would choose The Hostal Las Rosas, which one do you recommend? Also which is the restaurant you are recommending ? Also would we have a car which place is better to stay and park. Muchas gracias.

Hello, Graziella,
The restaurant is Rincon del Adarve.
Hotels/Hostales I dont know as I do not spend the night there; but I have a friend who lives in Priego and shall contact him. It may take several days, but I'll be back with this info.
Parking, well, I know the tricks to park there. I'll send you details. Priego is on top of a low hill, but high enough to park and walk upwards.