There is a wonderful self catering accommodation in Lagos called the Dona Ana Garden. It is a very quiet, out of the way spot, but only a two minute walk to one of the loveliest beaches on the south coast. In fact, that is not just my opinion, but it actually placed in the top ten beaches of Portugal. This is a small complex, comprised of buildings with four or so units. Different units have different personalities, I know because we spent a ton of time staying at this place when we were waiting for the sale of our home to be complete. So, we have stayed in at least 4 of them over the course of several months.
The grounds have lots of beautiful flowers, vines and trees, and the centre of it all is the well maintained pool. Not to mention that the staff are dynamite, even if you do not speak a single word of Portuguese, they will patiently work to meet your needs. If we were to say we preferred one unit over another, it would probably be the ones facing the beach of course, especially those on the second floor. There are balconies equipt with seating that make for the perfect happy hour, and early breakfast set up. Of course all of this will be based upon the number of rooms you require, they have studios, 1 bed, 2 bed and 3 bed available.
This place is just a hop skip and a jump away from the historical centre, and with all the pastries you are bound to be trying, the walk will do you good. Thus, you can reach the nearby action quickly, and return to solitude easily.