The nearest one open right now is either Valencia

https://www.primark.com/en/store/valencia-bonaire

or Castellon

https://www.primark.com/en/store/castellon

also Barcelona

The Tarragona branch is rumoured to be open late 2016/2017 possible venue is here...

http://www.ccparccentral.com/en/stores/

Here is a translated snippet from a local rag....newspaper not an item from primark 

The works of Primark, next to Eroski, are under way for three weeks, and it seems that before Christmas, the low cost clothing store is already open to the public. According to local sources, the Irish brand intends to open as soon as possible. The new store will be installed on the ground floor, in the area where there was the Eroski supermarket, which reduced its surface a few months ago. Workers say Central Park three weeks ago have started the works, although a top structure plaster look inside the store. So far, Central Park and Primark have refused to confirm anything.

Last June, the local media since echoed the new openness of the Irish company in Tarragona, but did not know the date and location. And so as Central Park Primark wanted to take the opening process with the utmost confidentiality possible. Workers in Central Park, which for three weeks endure the loud noise of the works, ensuring that reported in early November will open. The Irish company of clothing, footwear and are looking for low cost personal via Internet to work in new stores, including Tarragona. As can be read on the website, "Primark is looking for dynamic, committed and enthusiastic, who want to work full or part, or only on weekends"

Hey Bunter,
If our job interviews are on the same day do you want to car share? 
Mike

I was opting for Out-sized Ladies' Department given my predilections. 

https://www.youtube.com/watch?v=ixb5YiscjMQ

Has Primark opened in Tarragona yet?