Cordoba as hub for Andalucia?

Most would probably say Sevilla, but you should make a list of what you wish to see in each place. The travel time between Cordoba and Sevilla is minimal, but I would look carefully at Granada travel time before deciding.

ETA Also consider how you will get to Lisbon--bus or flight (from where)?

Personally, I wouldn't do any of them as a hub/day trips. Granada isn't close to either Cordoba or Sevilla. You would get more out of these town by packing efficiently and lightly, and spending a night each in Cordoba and Granada and two in Sevilla. In stead of doing a round trip each day, you would have half the transportation time. I still don't think its ideal, but I think this would be the best option. I'd start with Madrid, then Cordoba, then Granada and lastly Sevilla where you could fly to Lisbon.

Make sure to purchase Alhambra tickets in advance.

I love all three towns, but out of the three I would not pick Cordoba as a base to see Granada and Seville. So difficult to pick with only 4 nights you're going to need to rush, only two nights in either Seville or Granada is a pity as they both deserve more time. When you move around too much you don't see more, you see nothing. I like to be in Granada on the weekend as that is when all the locals dance in the square, there are bachelor and bachelorette parties, and the place is just so much fun. Seville is wonderful all the time, even during Holy Week when it's packed. For me with only 4 nights I would stay either in Seville or Granada and save the other city for another trip. Seeing Cordoba as a day trip would then make some sense in a time-line, bang for your buck situation. J

Personally, I would opt for 2 and 2 in Seville and Cordoba. There is much see in Seville but you can cover a lot in two days. Cordoba is not to be missed. While both are awesome, I would choose the Mezquita over the Alhambra.

I’m not a fan of “hubs” for an entire region. I think you don’t get a feel for the real character of a city on a day trip focused on “must see” locations. For me, part of the appeal of Sevilla and Granada is in the evenings, at least to me, the evenings in Sevilla and Granada are preferable to Córdoba. As already noted, some of the cities are not close and you might spend as much time traveling to and from the “hub” as you do on the day trip locations.

Archimedes, I agree. I understand the appeal of a "base" or a "hub", but often, I feel the vibe of the city is lost when missing the evenings and mornings.