Southern Spain in March/April/23

It will depend on your ultimate itinerary, but don't be so quick to think driving will be of benefit. I am actually a fan of driving trips and did one in Spain last May, but for Andalucia, it would not be my first impulse. Perhaps once you flesh out which places you will stay, you can determine if a portion of your trip would benefit from a car for exploring small villages.
To me, distances are such that moving bases is more convenient than day trips (exceptions to every rule of course).
For seafood, I would look at either side of Cadiz, but we've eaten great seafood even quite far from the coast. The area around Zahara de los Atunes is known for its tuna fishery.

Others will comment on Easter, but other than that consideration, I think it's a perfect time to visit.

Andalusia gets crazy busy at Easter, better get your hotels now and understand that you will probably pay double the regular rate. Schools and businesses have a long, long holiday week so trains and buses will be packed. But I also think Andalusia can be done by rail.

That said, being in Southern Spain at Eastertime is a once in a lifetime event. I stayed in Seville around Palm Sunday and seeing the processions, and being with the crowds was magical. Plus all the wonder Spanish Easter treats.

As Heather said, Easter is super busy in Andalucia. And it's not the Easter weekend- it's a week+, with everything fully ramped up by the Friday before Palm Sunday.

The way the express rail lines are laid out, it's easy to travel from Madrid to Toledo (on a spur line that doesn't extend south of Toledo); to Cordoba, Seville and Jerez/Cadiz; to Cordoba and Granada; and to Cordoba and Malaga. To connect places in different groupings (most commonly folks want to travel between Seville and Granada) by train, you often need to go back to Cordoba and change trains. Though the trains are fast, the layover adds time, so many folks choose the option of renting a car for the east/west part of the itinerary, which allows for stops in Ronda (which has limited rail service) and one or more of the white villages (e.g., Arcos de la Frontera, Zahara de la Sierra and Grazalema--which have only bus service, often infrequent).

Although you can get to those white villages (and more easily to Ronda) without a car, attempting to do so on a short trip is likely to lead to insufficient time left for the much more important destinations in Andalucia (Seville, Cordoba and Granada). Although Ronda is a bit of an exception, the white villages I've mentioned are known for their picturesque, white-cube architecture rather than for being sight-rich. With the amount of time you have available, I think it's going to be difficult to allot sufficient time to Madrid, Cordoba, Seville and Granada and have days left over for smaller towns.

How many nights will you be able to spend in Spain--not counting the night on the plane?

Andalucia is large, and I really don't think it's practical to pick one base and do a lot of out-and-back daytrips. If you were doing a long-term house swap in the area, that would be different, but there's tons to see in Andalucia, and you don't have much time. You can explore estimated driving times on the ViaMichelin.com website. Note that those projected times do not include stopping, getting lost, traffic delays, looking for parking, etc. For comparison, take a look at the train times on the Renfe website.

Regarding hotels: Availability and price are both issues during Holy Week in Andalucia. In Seville (April 2019) I had to pay about double the usual rate, and I had a 14-day cancellation period where normally I'd have been able to cancel up to 3 days before arrival. It wasn't easy to find something affordable (I'm cheap), even looking about 3 or 4 months in advance.

I've visited Andalucia 3 times. I only rented a car (twice) to explore the hill towns, based in Ronda. Otherwise, trains are faster and more comfortable. Use taxis to get to/from the train stations - they are not expensive.

Semana Santa begins on Palm Sunday, April 2, 2023. During that week, many streets in the historic centers of Andalucian towns will be closed to vehicles - some streets for the entire week, some only when processions are scheduled (which could mean a longish walk on cobblestones to your centrally-located hotel. I've been to Malaga and Sevilla during Semana Santa - I'd avoid Sevilla that week. OTOH I loved being in Malaga for the celebrations. As others have said, Semana Santa is very high season in almost all of Andalucia. I left Sevilla on Saturday afternoon for Cordoba. Easter Sunday there was not at all crowded and my hotel didn't charge much over what I would have paid a month earlier.

Supermarkets and grocery stores will be closed on Easter Sunday. OTOH you may need a reservation for dinner - everyone seems to flock to the restaurants - and all are open.

Semana Santa is a full week of festivals and parades, not merely Easter weekend. In the smaller towns, its a pleasure.

In the larger cities, it is both exciting and very crowded. The night of Palm Sunday, it took us a couple of hours to find our way around the procession and through the crowds to walk about four blocks back to our hotel near the Mezquita in Cordoba.

Thank you. This is great information as I am
planning the same trip in the spring.

FYI if interested

Spanish school holiday dates 2022–2023
Easter break: 1–2 weeks between 30 March – 17 April 2023

Holy Week April 2-9,2023