There are hundreds of km of marked trails. Other than August when it will be too hot, you can explore them all year round. Many are along the cliff tops so stabilising poles if you are getting unsteady and shoes that grip the loose footpaths are needed. Land slips are common so watch out.
Quiet local walk
This is 5km from Quinta da Fortaleza and is a beautiful walk starting with a path down a gorge to the coast. Park by the bus stop or down a single lane road ending in a muddy parking field. There are no towns or developments at all on this excursion. You will need to do it an hour either side of low tide unless you want to wade across the headlands – ideally at spring tides (maximum difference between low and high tide). You can check these here Tide Times and Tide Chart for Lagos (tide-forecast.com)
Wild and rugged!!
This is a fantastic walk with no developments other than 2 cafes which are open in the height of the summer season. Good car park at the bottom of a very winding road. Can be done at any state of tide.
Alvor and Lagos
There is a new broadwalk that starts near Lagos train station and goes for miles to the entrance of the Alvor lagoon. There are many beach cafes and restaurants along the way. Also recommended is the Alvor broadwalk. Start by the fishing huts (good parking) and head west – the path is obvious. There are a couple of other walks around the lagoon (well known for oysters and many other shell fish) – ask me for details