Seville, Cordoba, Granada, Gibraltar, Arcos de la Frontera,

Matt brings up a good point. It is ESSENTIAL that you book ahead for the Alhambra...or you likely won't get in. Access is strictly limited to a certain number of visitors per day. There's a morning and an afternoon session, each of which also gives you a half hour time slot by which you MUST begin your tour of the Nazrid palace. Tickets can be had here.

OK...suggested itinerary....Madrid, at least two nights.....Madrid-Cordoba by train (2 hours, overnight)...Cordoba-Granada (2:20 by train, 2 nights)....Granada-Sevilla (train or bus, time for both about 3 hours, cost about the same, but buses are more frequent and quite comfortable....2 nights in Sevilla.)
In Sevilla, rent a car. Drive down to Arcos (yes, it's worth a stop) for an overnight (less than 90 minute drive), then drive to Gibraltar the next day, park in La Linea, and walk across to catch the city buses (blue) with an all-day pass (follow Rick's instructions) or the red double-decker tour buses. Then drive back to Sevilla that night. Travel time Arcos-Gibraltar, about 2 hours...back to Sevilla, about 2:45.
The rub comes in getting from Sevilla to Lisbon. The transportation links between Spain and Portugal are abysmal, except for the roads....and you'll incur quite a penalty if you rent a car in Spain and drop it in Portugal. If you don't want that expense, then you'll have to take the bus into southern Portugal and up to Lisbon, or a bus across the border to, say, Faro, then take a Portuguese train to Lisbon. It'll take most of the day for that journey.

I recently returned from Seville, Cordoba and Granada and found it easy to travel between cities on public transportation. We took a bus from Granada to Cordoba, which I highly recommend for the spectacular scenery. Between Seville - Granada and Cordoba - Sevilla we took a train, which was easy and comfy.

Wonderful, friendly people in these towns, in addition to the outstanding Moorish architecture!

Try to arrange your itinerary so you're not seeing the Alhambra on the weekend--it's understandably popular.

Norm's advice is spot-on (as usual). For the tricky part - getting from Seville to Portugal, drive your rental car to Huelva, the last town on the Spanish side of the border with a rental car agency, and drop it there. Bus to the border, walk to the river, then take the little ferry across to the Portuguese side. Then bus again to Faro, where you can pick up your car for Portugal. Drive to the Algarve and enjoy a couple days there, before heading north to Lisbon. Drop the car there.

We did this (although in reverse order, we were coming from Portugal and headed for Arcos) and it worked, although the day when you cross between Spain & Portugal was mostly lost to transportation (and involved a lot of different modes of transport!). Still, it allowed us to save like $600 (the drop-off fee we would have had to swallow). I'd do it again.

Oh my gosh, thank you so very much for all your suggestions on when to drive, when to go by bus/train. We will need to look carefully at our plan again with a new perspective. Thank you, thank you, thank you

My suggestion would be to stay in Ronda rather that Arcos. We just did both...loved Ronda but felt like Arcos was not worth it. Ronda is beautiful. YOu can take a short hike down the gorge to view the bridge. The town if very enjoyable, you feel like a local not a tourist.

I guess tastes vary. We absolutely fell in love with Arcos, and thought it was utterly magical, one of the highlights of our trip.

We thought Ronda was OK, but nowhere near as charming as Arcos - not even close. Yes, the bridge and gorge were cool, but we had the sense that Ronda was crawling with day-trippers from "the costa del sol" and was way more touristy. Arcos seemed a lot more authentic and less crass.

I guess the best plan is to go to both and see which you prefer.