My wife and I are going to southern Spain along the Mediterranean coast in February. What two towns would you pick along the coast that we could stay in for seven days in each town? We’re looking for accommodations that will allow us to go to the market during the day and pick up some fresh fish and vegetables and come back to the apartment and use a full kitchen. Some nights we would also go to restaurants in the area.. what two towns would you recommend to experience the culture of southern Spain along the coast?
You will probably get great options from locals. In the meantime for those quantity of days, I would pick Cadiz & Malaga.
I would recommend Malaga as one of the towns. Malaga has a beautiful, pedestrianized historic center, which has been tastefully restored.
For sightseeing, here is a sampling of interesting and beautiful sights:
Catedral de Malaga
Museo Picasso Malaga
Alcazaba
Castillo de Gibralfaro
Mercado Atarazanas
Stroll along the seaside promenade and have drinks while watching the sunset.
There are more museums you can visit (art museums, history museums), but we didn't have time for them.
I know a few people who have spent a week in Malaga, and they have also included daytrips, so you could always do that if you are interested. Granada is about an hour to 1.5 hours away by ALSA bus or train so that could be a possible daytrip to see the Alhambra. However, I think it's more enjoyable to spend a night or two in Granada.
Another vote for Malaga!
Towns or cities?
Málaga and Cádiz are cities that have what you’re looking for. Most of the small towns along the coast shutter after the tourist season, so may not have enough to do or see for a week. Towns along the Costa del Sol will be open, but won’t have the authentic Spanish culture you’re looking for.
If you want an actual working "white" town, as opposed to a tourist-oriented town, you could consider the fishing port of Barbate, which is on the Atlantic Ocean and would make a good second base after Malaga. There is a good daily food market in the center, and several excellent restaurants featuring the famous tuna of this coast. Prices should be extremely reasonable in February.
https://www.taste-adventures.com/post/taste-of-a-place-barbate
Another good option, about ten minutes inland from the coast, is the "white town" of Vejer de la Frontera, which is extremely beautiful, has many good restaurants, a food market and small food shops, and is within an easy drive of many interesting sites: Roman ruins, bird-watching areas, coastal walks, etc. You should have a car to base there, however.
More info on this region:
https://community.ricksteves.com/travel-forum/spain/province-of-cadiz-some-information
Are you planning to "live like a local" or use the town as a base for day trips? My experience in February is that there's not much to see or do along the coast and not at all scenic. I'd point out that Cadiz is on the Atlantic coast but still a good option.
There are nice day trips from both Cadiz and Malaga but inland, not on the coast, except possibly Gibraltar which may be too long a journey by public transportation to make it a worthwhile day trip.
Just to add that the places I mentioned in my post are fine in the off-season; I visit in March every year.