Transportation in Southern Portugal and Spain

I think you mean Sagres and Salema as a day trip from Tavira - if so this will occupy much of your day in travel! but - the rail network will take you to Lagos http://www.cp.pt and there are buses from Lagos with http://www.eva-bus.com/novo/index.php to Sagres and Salema. The same bus company will take you Tavira to Seville, where you take a bus with http://www.tgcomes.es/horarios_33_english.htm to Tarifa. Tarifa to Cadiz with http://www.tgcomes.es/horarios_14_english.htm For Arcos - Tarifa to Jerez with http://www.tgcomes.es/horarios_33_english.htm and Jerez to Arcos with http://www.losamarillos.es For Granada - Tarifa to Algeciras with http://siu.ctmcg.es/en/horarios_lineas_tabla.php?linea=7 and Algeciras to Granada by train http://www.renfe.com/ or bus http://www.avanzabus.com/web/default.aspx Does this cover all?

My Brother has lived in Tavira for the passed 5+ years, he doesn't have a car and uses public transport to get around, I'll e-mail him and see what he has to say:)

My Bro says... Train! still cheaper than bus even if they don't have a passport to show they are over 65. The out of the way places like Salema and the short connection with Sagres may be best connected by coach or bus. Car hire is not expensive and could be worth considering if they are going to make a lot of short visits for exploration.
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Teresa Bellingham - please acknowledge you returned to see the effort and information provided for you.

Thanks so much - your information has been most helpful!

Thanks for the thanks.