Depends where you are staying and if you have a car.
One of my favorite local Portuguese restaurants is Prato Cheio. See this article on my blog which has a link to it.
http://barlaventostravelblog.blogspot.com/2009/01/restaurante-o-prato-cheio-lagos.html
If you like fish, try a bacalhau (cod) dish, if its on the menu. The Portuguese have at least 365 ways of preparing them. My favorite is Bacalhau à Bras.
Many Portuguese restaurants have "Pratos do dia" - (Daily Plates) or Menu of the Day. Usually freshly cooked and very good. I would recommend avoid dishes with "Grão" or meat dishes called "Rojões" until you acclimatise.
Another good local restaurant is "Os Asinhas".
Map ref here:
http://mapas.sapo.pt/?M=37.096817,-8.673522,16,Z;37.096817,-8.673522,As+Asinhas,1
Estrada da Ponta da Piedade,
lote 24, loja A
Lagos
The two restaurants above are outside the city wall and away from the tourist centre...which is why I like them! :)))))))
