If you look further down the site for a topic called Cabanas/Tavira started by Globalnomad, you will see a list of places that I think are well worth a visit to in the Eastern Algarve.
If you are driving, I would also recommend that you visit the west side of Faro as you have never been to Portugal. The east and west are very different IMO. Both having their own distinct charms.
Wherever you go, I'm sure you will fall in love with this beautiful country and it's friendly people and like most of us, become addicted to it, returning year after year!!!!!
Pat
