I don't know what kind of cycling you like, but here's what I experienced: the Algarve coast itself is not a good place for cycling: way too densely populated and too much, often hazardous traffic, especially during the British holidays, when "every drinking village has a fishing problem (read that on a Tshirt). There's an incomplete Eurovelo cycling route (EV1) that follows the coastline. The western-most part of the Algarve OTH is a very attractive Natural Park and the stretch of Atlantic coastline there is one of the most beautiful in Europe: west of Lagos, to "the end of the world" in Cabo Sao Vicente and then all the way up north to Sines. Highly recommended, there's lots of unpaved roads so some type of hybrid or gravel bike gives you the best options - no skinny tires. For serious climbing you have the forested mountain range of Monchique (900m, 3000 ft), a classic cycling destination north of Portimao. East from Faro, riding is much more fun some 10-15 miles inland. Just a frisbee's throw from the coastline sprawl, you enter a remote region with dusty, sleepy villages and virtually traffic-free little roads aplenty. I did like that part very much. In Alcoutim you can get across the Guadiana river into Spain by water cab.
Some pointers for gps tracks (or map info): "Rota Vicentina", along the Atlantic coast, "Via algarviana", off road cycle trail parallel with the coast, "ecovia litoral", basically the EV1 that runs along the coast.
Close to Cape St Vincent
Seriously funny German expats
Alcoutim: looking at Spain
