Itinerary Suggestions - Where to start?

Before renting a car, I think you need to decide where you want to go. Spain's public transportation in quite good. Portugal is not all that well connected to Spain via public transportation, unless you fly, perhaps. Definitely no car for Barcelona. Even if you want to explore outside of Barcelona like Montserrat and Girona and Besalu, there are trains and buses to get you there.

We flew in and out of Madrid, because we can find better prices and flights. You can construct a circle from Madrid so that you are not backtracking. We haven't spent much time in Madrid, we took a train immediately from the airport to Sevilla. Or you could fly into Barcelona (or out) and then fly out of Madrid or Sevilla. You really need to decide where you want to visit, first,

I am very visual. The first thing I would do is look at guidebooks with pictures (Eyewitness Travel can be good) and watch the Rick Steves shows, and YouTube videos. You can start here: https://www.ricksteves.com/europe/spain You will find the shows and other information there. You can also find the Rick Steves shows on PBS passport, Amazon Prime, I think Netflix, and probably also at your library.

Apologies if the following isn't helpful
a) I don't know where you are travelling from, but if the Americas then your easiest/direct flights might be to Bardelona and Madrid (plus Lisboa if going to Portugal)
b) a car makes sense if you plan to visit smaller/rural places but if you fix on the larger towns and cities, then public transport could be better
c) with 4 weeks you can certainly see part of Spain and part of Portugal. But don't fall into the trap of looking at them as day trips from each other. Whilst with a car, you easily cross between Extremadura and Evora (just examples), distances and poor cross-border public transport mean the two countries cannot be treated as interchangeable.

Just as a start. Since you mention the south, I might start in Madrid (1 week with day-trips by train), then train to to Andalucia (2 or 3 week tour by car/train/bus), then train or aeroplane to Barcelona for a week with day-trips by bus/train.

We have similar interests and recently flew to Barcelona 7 nights, train to Seville 5 nights, bus to Granada 3 nights, train to Cordoba 3 nights, train to Madrid 5 nights (day trip to Segovia), flew home from Madrid. The reason we spent so long in Barcelona was for a festival that was a trip highlight. Check out La Merce Festival which appears to be Sept. 20--24 and try to see the fire parade and other events. We also enjoy villages but didn't get to see any because there we prioritized seeing the cities. We usually rent a car and drive all over the place but enjoyed using trains and buses. I wanted to include Portugal but my husband didn't want to be away from home for longer!

These are all great suggestions!
Nick, I should have included that we will fly from either Atlanta, Ga or Charlotte, NC.

Jules & Cindy, these are great suggestions. We will explore Barcelona and Madrid, if we fly in/out of that city. However, we want to concentrate our time on smaller villages. I like the idea of a circle and no backtracking. We also like the idea of several days to a week in one place and day tripping from there.

We are very familiar with Rick's books and shows as we have been following them since our honeymoon in 1990. That's when he had the 2 - 22 Days in Europe (and other countries) books. I still have them and enjoy flipping through them occasionally.

There are small towns you can visit from Barcelona. Girona is about 100,000 and Besalu is about 3000. Besalu is a day trip from Girona. You could day trip to Girona from Barcelona, but we stayed 3 nights and wished we'd had 4. Other towns from Girona could be Figueres and Cadaqués.

We stayed in Cordoba, one hour via train from Sevilla, for 3 nights and would have liked 4. We adored Cordoba. The old Jewish quarter was spectacular. In addition to the amazing Mezquita, there are white homes with gorgeous patios. Between Sevilla and Granada are the pueblos blancos. Small white villages. We liked Zahara, Grazalema and Sentenil.

to smaller places, ....light hiking, walking and exploring villages.

The first thing that came to mind is the Cinco Villas of Aragon.

After exploring Barcelona, you could take the train to Zaragoza. It is an underrated city, and if you search the forum you will see that people recommended it. After a two or three days, you could rent a car and head north. The Cinco Villas are some surprising little towns in Aragon. Full of history, and devoid of tourist. I loved Uncastillo. Finish the day in Sos del Rey Catolico, at the parador. Sos is the birth place of Fernando of Aragon, on of the "Catholic Kings".

The general area is full of sights and small villages. There is the castle of Javier, and a bit further on the Castle of Loarre. You could visit Jaca and the monastery of San Juan de la Peña. Etc...

You could then go back to Zaragoza, drop of the car and take the train to other Madrid and beyond. Or if you want to road trip more, head into the province of Soria and follow along the Duero river. There are some beautiful towns there too. I really like Burgo de Osma as a place to stop.

Just a general heads up, the 21st is Saint Mathew's day. Here in La Rioja/Logroño it is celebrated as the wine harvest, but in many places around Spain they celebrate St. Mathews too. Around the same time, the 24th, there is the La Mercé in Barcelona, and it will have it's associated fiesta.

Dlindstrom, thanks for the heads up re: holidays and celebrations. All the small villages you described sound wonderful. We will look at a map to get a better idea, but you have great ideas! Thanks!

three weeks gives you time to see a lot, especially stuff of the beaten path.

Gotta agree with dlindstrom. Cinco Villas is a wonderful option Olite is another amazing pueblo in the area. Aragon and Navarra are both filled with amazing sites that are off the guide book radar. Well worth looking into... there is so much more to Spain beyond Barcelona/ Madrid /Andalusia(all worthy).
Brad