[Fluivelip]

Grupo Soledad are the big tyre people round here. Confortauto
is one of their brands, and they have a "Localizador de Talleres (find your nearest garage)" on their website...
http://www.confortauto.com/
just pull down Alicante and you get a selection.

And I'm reliably informed that their re-threads are very good ;-)) although they do all kinds

and if you want to impress the locals with your in-depth Spanish vocab, the word for re-threads is "Recauchutado"

... only thing is that I'm not sure if the English is so spot-on