Totally Torn

Either itinerary would be lovely. Your assumptions about variety of landscape are not necessarily wrong. But I'm also thinking that the northern Spain combination makes most sense. If pressed for time, you could cut Algarve, since you'll have other coastal stops.

Here's one route suggestion off the top of my head: Fly into Faro, if including the Algarve, or fly into Lisbon and consider making your first north-bound leg to Coimbra by train. Skip over Porto initially and head from the Douro Valley toward San Sebastian, then circle around toward Santiago (the direction of visit for an old-time Camino traveler), then drop car in Porto and fly home from there. This avoids the second-country drop fee, and avoids back-tracking all the way to Lisbon.

When you to return to Spain, the southern destinations are easy to include. For instance, if you fly into Madrid, then train travel times to Cordoba, Granada, and Sevilla take about half as long as would train travel to San Sebastian or Santiago de Compostela.

A couple of comments but either trip will be quite nice.

In Andalusia, Granada is a must, IMO, not a maybe. The Alhambra in Granada is one of the most spectacular sites in the entire Iberian peninsula. Gibraltar is very much a maybe. I did not think it was worth the time and effort to get there.

And, while Andalusia is a lovely area, it will likely be more like much of Portugal than the Basque Country. I was in the Basque Country a few years ago in May (late May) and the weather was good. It is green and lush and somewhat reminded of Switzerland in some areas. Both Andalusia and much of Portugal are much more arid. All three areas are very unique, culture wise.

Either trip should be great, but I would lean slightly in favor of the Basque Country.

As you continue to dig into guidebooks and online references, I think you're going to find your time allotment will require some corner-cutting just to cover the areas you've mentioned. Then there are places you haven't listed that are more or less along your path. Those include Evora and Sintra (among others) in Portugal and a whole string of interesting places in northern Spain between the coastal Basque Country and Galicia (including Vitoria-Gasteiz, Burgos, Leon and the gorgeous Picos de Europa area). I'd cut the Algarve for sure. I haven't been to Gibraltar despite having recently spent 4-1/2 months in Spain, which tells you how comparatively (un)interesting it sounds to be. However, you mention a daughter. If she's fairly young, the Barbary apes might be a hit.

I don't have a preference between Andalucía and the Basque Country+Santiago de Compostela. The Basque countryside is beautiful, and if you're looking for variety of scenery, the Picos de Europa area is even more spectacular. I think in terms of scenery, northern Spain will allow you to see more loveliness than the usual quick trip to Andalucía that mainly hits Seville, Cordoba and Granada (which is pretty much all you'll have time for). From the architecture standpoint, I'd say Andalucía is more distinct, though there are a few modernista buildings across northern Spain; I've seen them in Comillas, Astorga and Leon.

It will likely be getting rather warm in Andalucía by the time you land in Europe, so be sure to put Andalucía first if that is the area of Spain you decide on. Granada will probably be your coolest stop down there due to altitude.

Thank you all. After reviewing flights, Rental cars and a few other factors we have opted for the Southern Spain option with flights into Malaga
My daughter spent a term studying in Granada 2 years ago so she is somewhat familiar with much of the area we will visit. Oddly enough the rental car was less expensive to pick up in Spain and drop in Lisbon than pick up/drop off in Lisbon. I gather rental cars in spain are just generally less expensive than portugal so even with the one way eu300 drop fee it was still a great deal through Gemut Travel in Oregon. (Plug)
Im looking forward to our trip and know its going to be great. My daughter will join us flying in from Paris and shes also fluent in Spanish so thats a plus for us since we are not...lol
Thanks for your replies. As Rick reminds us, we will go back, so next trip will include Basque country😁