EAS airport is indeed poorly communicated, but you can get on an hour long bus ride for cheap at be at BIO which has connections all over. Pretty much all of Spain has a great bus system so getting to airports isn't that big of a deal.
It is a special city, though the language issues aside there is a definite Basque culture which is pretty much nothing you think of when you think of stereotypical Spain. The image sold to the outside world is generally of Andalucía, so if you want that sort of experience, Sevilla is probably the best option.