Itinerary advise - Algarve or Gibralter in mid to late March

Gibraltar is a half day visit.
Algarve you can spend many days depending on your interests.

Rick usually compares Algarve cost to Costa De Sol of Spain (derisively of course)

Find out from your rental company if their contract will allow you to drive into Portugal Some do not allow you to cross national boundaries due to insurance reasons

If you are coming from Seville towards Gibraltar, you may want to combine trip with Cardiz or Ronda or Sample Costa De Sol or also visit Cardoba and Grenada.

I would definitely prioritize Cordoba and Granada over Gibraltar or the Algarve. Cadiz is also a good option. A car wouldn't necessarily be useful for you if you substitute those world-class cities for Gibraltar/Algarve, and you won't want to use the car while you're in Seville; you'll just be paying (probably) to park it.

Three days is a bit short for Seville. There's a lot to see there. In addition, if it's your arrival point on the Iberian Peninsula, you may be dragging a bit at the beginning of the trip from a combination of sleep-deprivation and jetlag. I never count my arrival day as a sightseeing day, because I know I'll be brain-dead.

thanks all! I will heed your advice.

Most people do not like Gibraltar.

The Algarve is nice but agree that there are more worthwhile places to see if you aren’t bothered about the beach or relaxing in a nice hotel for few days. Just driving around won’t be very rewarding.

My mistake for not giving you more information. We will spend two weeks in southern Spain in the Andalusian region. Our final destination in southern Spain is Seville before we drive on to Portugal. It was suggested to us by a tour advisor to then head to the Algarve region. But we're hesitant to go there due to it being mid to late March and we're not "into" beaches or laying on the sand!
I don't know what the scenery would be but it sounds from one reply that it's really not that interesting. So I'm stumped as to what to fill in between Seville and arriving in Lisbon (if we skip the Algarve region all together). Our Andalusian time is easy to plan but we want to include Portugal also and having a tricky time since we need to go in March. (And yes, our rental car is available to travel between Spain and Portugal. We plan to fly into Madrid for 3 days, take the train to Granada. We'll pick up our rental car when we leave Granada and tour the Andalusia region)
Appreciate your advice as always!

Mary

In between the Algarve and Lisbon you have the Alentejo region of Portugal. It’s a very unspoilt area with beautiful coastline. March is a great time to go if you want to do some walking and explore the interior as it gets very very hot in summer. You can enjoy the beauty of the coastline without lying on the sand. I have only been there once so I’m not an expert but would love to return. A good guidebook to Portugal will help you identify some highlights. You would need a car.

thanks Helen! I think that would suit us well.