Aún así meaning

Hi Shirley,

In the context of the text you're referring to, 'pero aún así ', in my opinion, means, 'but still' or 'yet still'.  So, in the passage... 

Like every year, I'll wake up with bags under my eyes and a hangover but I'll still (yet I will still...) go to spend New Years day morning with my grandfather.

I hope this helps. I'm pretty certain this is what it means. The lovely Inma will let you know if I haven't got this right.

¡Feliz año nuevo!
Clara :)