I was thinking of Cordoba. Also I've seen it mentioned before that driving in Seville is a nightmare. Any suggestions on safe places to park outside of town?

Cordoba . Also Ubeda and Baeza are two lovely towns to visit...and probably many more which I do not know.

Before getting to Sevilla from Cordoba , Carmona is a lovely little town with a very nice Parador.Osuna too is nice but not as exciting as Cordoba or UBeda+Baeza.

..and to give you a third reply, I like Jaen too. The Parador on top of a hill, next door to an old fortress is a wonderful place to stop. THe town Jaen is interesting too.

Taking the motorway A92, which is a more or less straight line Granada to Seville. The stop I recommend is Antequera. Other possibility is Osuna, further ahead. Both are monumental cities. A shorter stop can be made in Estepa.

Is the parador in Jaen as much of a hassle to get to as the one in Arcos? I could not get my car through the narrow streets and had to back down.

Carmona is not on the way to Granada. It is a nice town wich can be visited from Sevilla, going by local bus. There are plenty of them.It is just 30 kms far.

On the way to Granada, the first interesting town is Osuna, and the next stop I suggest you is Antequera, with wonderful churches and The Dolmenes, huge prehistoric constructions.

Sorry, I had considered the route Granada to Seville. Osuna is really beautiful, but if you are departing from Seville, I rec. Antequera. The dolmens are really huge, but they are subterranean, and have opening hours. Nevertheless there are many baroque monuments in Antequera to enjoy.