If you are planning to travel by Public Transport, strongly recommend you consider Lagos.
Faro has some historic sights but it is not by the Sea. It is inland on a lagoon. It can be visited in a day by train or bus from Lagos.
Albufeira, has good bus services but the train station is 6 km from town. It is also tourist heaven.
In Lagos, we have great beaches including the 5km long Meia Praia Beach, some wonderful views and the town itself retains a strong Portuguese flavour. However, our town council has taken upon itself to dig up part of our main avenida in at present as part of a town modernisation project. Nonetheless, I think it would be a great place to stay.
Have a look at these items on my blog:
http://barlaventostravelblog.blogspot.com/search?q=lisbon+lagos
As regards hotels in Lagos, have a look at the Albergaria Marina Rio or the Marina Club. You can find their details on this page or a Lagos-based event I am helping organise:
www.dancaiberica.org/index.php
Note that the Romatik is out of town and if you are not hiring a car you will be dependent on taxis or the daytime local buses to Lagos.
As regards taxis from Lagos Station or bus sstation...hmmmm!
Better pm me nearer the time with your details and I'll try to get one there for you.
