7 days in September-where to go?

That's a tough one. With just a week, I would do Amsterdam or Basque. For the latter, I would fly from Lisbon instead of taking the train from Madrid. 90-minute flight vs half-day train ride when you're already at the airport? Split time between Bilbao/San Sebastián and/or Biarritz/Bayonne. You could fly into Bilbao and out of Biarritz or vice versa depending on schedules.
A week is a long time in Amsterdam, which is very expensive, so a side trip would be a good idea. Where depends on your interests, of course, but there are lots of options within a short train ride.
I think Andalucia and Portugal each require more than a week.

Book your air tickets going thru Madrid to Granada, transfer in Madrid is easy. Choose to not check luggage and the typical 90 minute transfer time between flights is achievable. Be sure and you tube how to transfer within the airport WITHOUT EXITING into the arrivals area.

Stay in Granada three nights the. Take train to Seville and stay four nights.
Then fly from Seville thru Madrid back home.
We have utilized this tactic five times with ease and less stress than leaving the Madrid airport to catch a train.

September may still be hot in Andalusia and Portugal. I vote for a week in Amsterdam. You can do day trips to Haarlem, Delft, Utrecht, Leiden, etc.

"Basque country-with flight to and from Madrid" is a good option imo - it has an interesting own culture and hopefully more moderate temperatures in September.

Thank you all for your thoughtful and helpful advice.
The reason I proposed the above is that my husband is a reluctant flyer and will not do an additional flight after the international flight.
Seems like the group is generally in support of the Amsterdam/side trip itinerary except it is expensive.
Do you feel that the train to either of the two mentioned regions of Spain would be prohibitive time wise? Or is renting a car possible or advisable?

I opt for Portugal for the week. Fly into Lisbon. The trains are convenient. Three days in Lisbon and three days in Porto, one day in Coimbra. Sintra and Evora are day trips from Lisbon. It is more economical than Spain, the weather isn't as bad as the interior parts of Spain (coastal breezes), no flights necessary within the country. The train ride from Lisbon to Porto is about 3 hours. This would be your longest internal journey. Youy could go immediately to Porto (my option), then back to Lisbon to finish the trip and be on the ground for your return flight home. (Stop iin Coimbra on way back to Lisbon, about one hour by train from Porto. Coimbra to Lisbon is less than 2 hours by train.
We really loved Portugal hen e went. It was full of things to do, yet laid-back at the same time.

For clarity, the plane from Madrid to Granada is a 737, also from Seville to Madrid.
However, you can get from the Madrid airport to the Atocha train station and take the high speed train to Granada. Same for Seville to Madrid.
For us a bit more hassle to take the train and the expense, plane vs train, is essentially equal.