Use ViaMichelin.com for estimated driving times to places you'd like to explore in Andalucia. Of the big Three (Seville, Cordoba, Granada), Granada seems to be the fastest by car at less than 1-1/3 hours. Cordoba's closer to 1-1/2 hours and Seville's just over 1-1/2 hours. Seville in particular is a multi-day sort of place because of the number of sights and the size of the city. I always suggest at least 4 nights (3 full days) in the city, but with free accommodation not terribly far away, you might try to get an early start and just spend two nights in Seville. I wouldn't be happy with just a day trip to Cordoba or Granada, but I'm not the one with a free place to stay. Malaga is a very pleasant place to hang out, so I imagine you'll be hopping on a train from Antequera to Malaga often. I don't know whether there's any bus service from Fuente de Piedra to Antequera; you might need to drive and park the car near the train station.
Ronda's not much more than an hour away by car (more like 1-1/2 hours by train, maybe) and you could see much of what it has to offer on a day trip. Less well-known places you might explore include Priego de Cordoba (to which you'd probably have to drive) and Antequera. Antequera's quite close to Fuente de Piedra. You'll probably be visiting Antequera often, because it has a train station (FdP doesn't) where I'm pretty sure you can pick up a train to Malaga, Seville, Cordoba or Granada. It's possible trains will get you to those cities faster than a car. You can explore schedules on renfe.com. On some trains you can potentially save a lot of money by buying your tickets early, but take note of the change/cancellation policies for the various types of tickets.
I'm hoping some of the people on the forum who've driven in Andalucia will be able to suggest easy, short day-trips to places not far from where you're staying.
I don't recommend Tangier or Casablanca for a trip to Morocco. It's a fascinating country, but those are not among its most interesting cities. Tangier is like a border town, and Casablanca is quite modern. Places like Fes and Marrakech would be better targets. They have flights from a number of European cities, so they can be incorporated in a later trip. You don't have to settle for Tangier and Casablanca just because you're going to be in Spain.
