Bikes can be hired from the nearby Hotel Maritur, which is at the top of the road that leads into the Sao Rafael resort. They are semi road-mountain bikes and ideal for touring around. Be prepared to haggle on price, particularly in the low season, it is amazing how low the price can go from what you are quoted originally, and you can get better deals for longer hires.
A good ride to start with is Sao Rafael to Amacao do Pera. You can do much of this along very quiet roads. From the resort head out towards Gale. Just before Gale take a left turn towards Salgados. From then on hug the coast as far as you can, passing through Salgados. There are a number of beaches along the way, some with cafes and restaurants if you feel like stopping off. Just before you get to the roundabout to turn right for Amacao do Pera there is dirt track on the left hand side, just past a bridge. Take this and avoid the big hill into Amacao do Pera! This track keeps you on the level and goes right into the town. There are lots of shops, and restuarants where you can fuel up for the trip back. This is a nice light ride, and you can probably get to Amacao do Pera in less than one hour.
Another trip you might like to do is to cycle to Silves. This is quite a bit further, and hilly. And you can always cycle to the Marina or into Albufeira.