Minors under 14 are now allowed ourt for one hour per day all over Spain as long as they (and their parents) respect safety distances and stay within a one kilometre radius of their homes. The first day of this opening up was largely a success although there were well-publicised examples of careless disregard for the rules all over Spain.
The government plans to extend this freedom to adults who want to exercise or walk from the second of May provided that Spain's Covid-19 case numbers continue to drop. Adults will be allowed to do run or walk along provided that they stay within a radius of two kilometres of their homes.
A Canary Islands government proposal to start more general opening up measures has so far been dismissed by Spain's central authorities. Madrid has been clear that it will allow regions to open up at different rates depending on infection rates but only by following a national plan. This is expected to start after May 9th when the current extension to the State of Alarm ends. It is not yet clear whether Spain's government will extend the State of Alarm further in order to keep tight control over the opening up.
With the lowest infection rate in Spain, the Canary Islands wil be amongst the first areas of Spain to begin opening up. However, until we know whether the islands will be following their own plan or a national one, the dates of each stage of the opening up are not clear.