Southern Portugal is famous for its ceramics, and Lagos won't let you down. Ceramic dishes and tiles of all price ranges, styles, and colors are available. Some stores don't provide boxes for your goods, only newspaper wrapping, so ask before you buy, if it matters to you.
Portugal is also famous for its cork, in fact it's one of the largest cork producing countries on Earth. A short walk through almost any section of the town will reveal shops selling all kinds of cork products, from the usual coasters and placemats, right up to shoes, hats and handbags. Just as a note though, cork can be very expensive.
There is sometimes a small fair in front of the church near the harbor where unique clothing can be bought.
