I know the north of Spain, from the southernmost region (Andalusia) I have only been to Córdoba, which is beautiful but far from the eclipse.

I would look for any place that does not live exclusively on tourism, Cadiz or Algeciras, or rather some town that is not on the coast, like Jerez de la Frontera or Ronda, also El Ejido, which lives on greenhouses, but I think it has a little less time for totality.

I can't help you about the flights from Tallinn, but in any case that whole area is not very big, with a rental car from the airport you should be able to get around in a very short time.