Small city or town for one month between March and May

What are you interested in?

@Kenko makes a good point, a bit more information will probably get you a better answer.

For example, you say Spring, so that may include Holy Week and Easter. That may be a factor in where you want to go.
How important is food? Wine?
How do you feel about renting a car? While you will have a home base, you will probably want make some day trips or overnights. Most of those can be done with public transportation, but a car will give you more possibilities to visit smaller village and out of the way places.

That said, please let me suggest Logroño. It is the capital of La Rioja. It is a small city, but very walkable.

You can also make day trips to Bilbao, Vitoria, Burgos, Soria, Pamplona and Zaragoza.
There are wineries to visit, several in the city limits.

If you like hiking, there are lots of places around where you can take a hike/stroll through the countryside.
There is also a Michelangelo painting in the Concathedral.

If staying in one place, then things to ponder include size (big or small city? town or village?) and whether you will rent a car or stick to train/bus. Do you want a place large enough that you never have to leave (could be a big city or a small village if you want to hike, etc.), or that is well placed for day trips by public transport? All of that will affect the recommendations greatly. I know I would have a hard time choosing just one place!

You sound like us. We like to rent a place for a while and just hang out, see the sights at leisure, wander around, sit in a cafe people-watching. We don't jump from one place to another.

We spent 3 weeks in Seville in March 2025, renting an apartment in the Triana area, across the river from the main sights. That was perfect for us. We were right next to the Mercado de Triana. They have some great fish markets in there, along with the usual fruit and vegetable markets. There were some great restaurants and tapas bars right outside our door. There is a beautiful river walk all along the river. We didn't take any day trips at all.

We then spent a week in Madrid. Doing basically the same things.

I loved both places. You couldn't go wrong in either place. I want to go back to Madrid, because a week wasn't nearly enough for me. I fell in love with Madrid.

Seville should be warmer than Madrid.

Also, consider Toledo, Segovia, Avila, and Rhonda.

Unless you intend on having a rental car you should be in a location where there are plenty of transportation options; like those suggested by dlindstrom. If you will have a rental car, then look for locations where there are a lot of places nearby that are of interest to you, so you can make day trips. One month in any city or town is a long time unless you’re going to work every day.