With that budget you should not have a problem finding somewhere in Albufeira. Close to the old town might be a problem with the access as most of the properties in that area are old, not very user friendly. Their are some new ones in the town center though.

I am just about to buy a 2 bed apartment near the camera, just been renovated, new kitchen, two new bathrooms, new plumbing and electrics for 135,000 Euros so bargains can be found.

The most comprehensive site for finding properties is Casa.Sapo - Portal Nacional de Imobiliário: Imobiliárias, Apartamentos, Vivendas, Quintas, Escritórios, Terrenos e Imóveis de Luxo em Portugal ou no Brasil most agents have their properties on it, but it is only in portuguese. Alternativley an English portal with a few agents Algarve Property Database