For a few months I suggest Los Christianos in Tenerife but if you have all your gear and do not need easy access to a chandler then Santiago on La Gomera.
I have no knowledge of the eastern Canary islands.
Gomera is a bit out the way. The marina is good, and a place where a lot of people do their final preparations before crossing the Atlantic. It is also a popular place to leave a yacht. But when I was there about 4 years ago it was thin on facilities, and I don't think it would be ideal for lift-out/doing work. People seemed to have to take the ferry to Tenerife to collect orders.
Hi, There are no yards as you understand them in the UK and it is quite often more expensive on the hard than in the water.
Puerto Rico on Gran Canaria is the most convenient for yard services like water and electricity.
Puerto Mogan is the best though as the best chandlery in the Canaries is there.
Sunshine Maritime.
There is a new 70 ton travel lift. and the place has the worlds best weather, oficially.