Spain itinerary January and February.

Not unless you are driving I'd go straight to Toledo the first night you arrive and then to Madrid. There is no direct train from Toledo to Cordoba so you have to back track to Madrid to get there. From Cordoba I would go to Malaga first and then to Granada and then to Seville on the way to Lisbon.

I would add another night to Seville, Toledo and Madrid.

What do you want to do in the Algarve? It won’t be beach weather. I have been to the Algarve in February several times and now I head to the Canary Islands instead, as the weather can be awful in Portugal - very windy and wet. We have had sunshine too, but it’s warmer in Spain.

You maybe better either spending longer in Spain or heading to Lisbon and Porto and not the Algarve. If you are sure about the Algarve, I would head to Tavira or Lagos, as some of the smaller resorts close over the winter. You ideally need a car, which is cheap during the winter.

Jazz has a good suggestion about Toledo, but I'd want 2 nights there if it's your first stop. Otherwise, you'll basically just be recovering from the overnight flight and dealing with jetlag while you're in that wonderful city.

I don't know that it makes much difference whether your route out of Cordoba is Granada-Malaga-Seville or Malaga-Granada-Seville. Total train time is very similar, so I'd base the decision on train schedules (service in and out of Granada not being terribly frequent) and days of the week on which sights of interest to you are due to be closed.

Seville is a large city with a lot of sights, and I think you'll be very short on time there with just 3 nights. I'd extend that. By comparison, Cordoba and Granada are comparatively better covered with the time you have planned.

I'd want at least nights in Toledo even if it's not your first stop, though it's true some people manage with just one.

Although you might get by with two night in Malaga, it's not a small place. Any time you have just two nights in a city it's only one full day, and that can feel rushed. I try hard not to have any two-night stops.

I am not that much of an Algarve fan even at the optimal time of year (which is not Jan/Feb), so I can't really contribute much there, but as it stands you seem to be allowing 15 nights to cover five of Spain's most fabulous destinations and more than 10 nights on the Algarve (depending on how early you plan to be back in Lisbon). I'd definitely shift some time from the Algarve to Spain (starting with Seville and Toledo). Or to Evora. Or to Lisbon.

Other possibilities in Spain if you can be convinced that you've got an awful lot of time assigned to the Algarve would be Cadiz or a side-trip to Segovia from Madrid. Note, though, that central Spain (including the Madrid area) can be pretty cool in the winter. The average low temperatures in Madrid for January and February are down in the 30s. Seville and Malaga are about 15 degrees warmer. Granada and Cordoba cool off at night like Madrid.

I would add at least one night to Toledo. Otherwise it looks fine.

Just a added notes,
I arrive in Madrid at 9am. So the suggestion to go to Toledo is a great idea. We can get there at a decent time a see a few things. Go to bed early and hit the sites the next day.

I will add some time in Sevilla and add some time in the Malaga area. I will remove some time from the algarve…

I know that this is not the best time for the algarve. I have just been all over Portugal from Lisbon north.
I have spent winters in San Diego several years but it has got very expensive. The basic climate looks similar and the costs seems cheaper. We also want to check out the costa Azur and Algarve that’s why we left open some flex time while in Spain. Just looking at it as a place to spend winters

Well, that's a different matter.

There have quite a few threads in the past that touched on what the Algarve is like in the winter. You might be able to identify some of them by scrolling back through the Portugal forum. I'd start with threads that have either "Algarve" or "winter" in the title.

Pre pandemic, there was a large number of American and Canadian snow birders based in Cabanas near Tavira. Many return there each year.

Cabanas has an older village centre and some great cafes and restaurants, but there’s also lots of modern development. It has a better feel on the ground than it looks on Google Streetview. The beach is out on the barrier island, reached by a short water taxi hop or drive along to Barril, where you can walk out to the island or catch the small train. Cabanas has a railway station connecting to Faro, the western Algarve and towards the Spanish border, where you could catch the ferry and go for lunch.

The western Algarve can be very windy at that time of year. Cabanas is much less so and milder.