On further searching I have just about decided that Olhao would be a good place for carless travellers to be based - but all self-catering that I can find seems full for last week of Oct. I am wondering about Fuseta which has a few places and says it is 8 km away. Does anyone know the "lay of the land" here. What is it really like and does it have any public transport? Not sure of spelling - sometimes it appears as Fuzeta.
Pro tip
