Itinerary Advice - 16 days in Spain

Since you say that you already are locked into flying roundtrip from USA to Madrid, based on the cities that have direct flights to Menorca and your desire to go to either Andalucia or Basque here is a rough draft and you could do some day trips here and there depending

Arrive Madrid spend 3 or 4 nights
Train to Granada spend 3 nights
Train to Seville spend 3 nights
Fly to Menorca spend 4 nights
Fly to Madrid the day before your flight back

I more or less agree with Jazz. However, I'm wondering since you don't want to spend a ton of time in cities, if you might think about less time in Madrid. If you are interested in art museums, that would be a big reason to concentrate time there. If not, my suggestion would be to spend more time in cities that are (in my opinion) more culturally and historically significant. Consider staying a couple nights in Toledo and Cordoba. Both are smaller towns and super interesting. Toledo is situated at the top of a hill with amazing views. Cordoba has the Mezquita, a very historic and gorgeous old town and situated on a river. The homes in the historic old Jewish quarter are known for their patios and flowers. I think you could also get by with 2 nights in Granada and could well need 4 nights in Sevilla.

I haven't been to the north at all yet. I was told by a fellow from Bilbao that Sept-Oct is the best time of year to visit the area. I also got the impression that it's a lot easier with a car.

Before you decide, do look at this website where you can find the historical daily weather conditions for cities for any month for the past 10 years. This will give you a better idea of what to expect. And remember that when you're sightseeing, you are out and about in the sun and heat most of the time. Good news - ice cubes are ubiquitous and are served automatically with most cold drinks.

By beginning of September do you mean in a few weeks time? If so you need to get a wriggle on and decide/book urgently. Cheaper internal flights and better seaside accommodation will already be sold so you may need to compromise.

Minorca is delightful and has fine beaches. But there are beaches in Andalucia and the Basque Country too. You should check prices and travel time involved before deciding. As an alternative, for example, you could spend four days in Costa da la Luz or Costa Almeria which would then be easier to move onto inland Andalucia. That would be Granada, Cordoba and Sevilla, none of which are in any way similar to NYC. From each of those cities you can catch a train back to the capital for your flight home.

Madrid will also be hot in early September.

Thanks for all the recommendations. Really appreciate it.

We like to build in some wiggle room and just take it easy as possible so we’re going to do:

3 nights in Madrid
Fly from Madrid to Menorca - 4 or 5 nights there
Fly to Sevilla and spend the remainder of our trip in Andalusia.