In Barcelona dogs must be on a lead in public space, except in the spaces designed for them: dog areas and shared-use zones, where dogs may be off the lead during the hours each one sets. Check the zone's sign before letting go.
For long walks, the Carretera de les Aigües in Collserola, Montjuïc and Parc de la Ciutadella are classics, and in summer Llevant beach has a bathing area for dogs. But the daily walk happens in your neighbourhood, so it pays to find someone who lives close by, in Gràcia, Sant Martí or Sants.
On Guauly, walks are done by community neighbours for free, and you choose who. Pro walkers set their own price per walk.