It may be warm enough for the beach but don't count on the pool or sea being warm enough for swimming.
For markets have a look at these posts on my blog:
http://barlaventostravelblog.blogspot.com/2008/12/lagos-algarve-markets.html
and
http://barlaventostravelblog.blogspot.com/2008/12/lagos-algarve-portugal-markets.html
As regards culture and history have a look at this article on wikipedia.
http://en.wikipedia.org/wiki/Lagos,_Portugal
If you are interested in history, a visit to the Fort at Sagres where Prince Henry the Navigator, (Infante Dom Henrique), had his navigation school is a must.
