Algarve between December and May

Hi all,

My husband and I live in Amsterdam but hate the winter here. We love Portugal and have explored most of the rest of the country, and now we want to explore the Algarve with an eye to renting something for the winter months (December through April) and possibly buying at some point. We'd like your advice in preparing an itinerary for a scouting expedition/road trip in February.

Here's what we are looking for (and the things we want to avoid: 

Our ideal place is in a village or small town. We want to be immersed in nature, with cycling and walking trails into forests, hills, along rivers and lakes or the coast. Small cities are possible if they offer exceptional cultural activities and infrastructure and have peaceful and green neighborhoods. (I would put Amsterdam, Porto and Lisbon in that category.)

We want enough tourism infrastructure to make it easy to visit (e.g., hotels, restaurants, etc.), but we don't want a tourist resort that goes dead outside of the high season. Similarly, we love places which attract many internationals, but we want there to be a lively local Portuguese community that we can connect to (eventually in Portuguese). That's a delicate balance, as interest from expats can drive property values up and locals out.  

We like the old towns of historic cities and small villages with buildings and narrow streets dating from the Middle Ages (or earlier). We want to avoid the large tourist resorts, high-rise buildings and apartment blocks. 

It's best if the town is accessible by public transit from Faro. 

Any suggestions? Tell us your favorite places (or, conversely, the places we should avoid.)

At the top of our list so far, from east to west (roughly): Vila Real de Santo António, Tavira (and Cabanas de Tavira), Olhão, Silves, Carvoeiro, Ferragudo, Monchique, Lagos, Sagres. I believe most of these places remain somewhat alive all winter, but I'm not sure about the smaller towns and villages (e.g., Sagres and Monchique). I'll appreciate your advice.

On a related note, we're newly retired scientists/academics, and my husband is an avid golfer and padel player.

Thanks!

-Kimmen