Try the Brisa Sol or the Vila Gale Cerro Alagoa they are both situated at the approach to the old town coming from the Montechoro side.Or you could try the Rocomar or Sol e mar which are both in the old town & near the beach.In fact the
Sol e Mar is directly on the beach. Not sure whether they are covered by package holidays though.

The Sol e Mar only has an indoor pool - it doesn't have an outdoor facility as it is literally on the beach as Jayjan says.

Thomson Holidays have packages to the Rocamar, which has a small pool on the roof but it is next to the beach using the new lift or 100 steps.

The hotels in the old town are much older and smaller than those newer ones on the outskirts eg Brisa Sol and Cerro Alagoa and most do not have pools. The beach is very close by, sandy, safe and free.