I got my first check from Google for €79 but when I took it to my bank, turned out that they don't deal with checks here. How am I supposed to get the money then? Is it possible to exchange the check abroad somewhere? There are no other payment options for my country and lately they even started to allow Adsense on Estonian sites. If they allow us to put ads on our sites but there is no way to get the money, seems like a win-win situation for Google, at least until webmasters get their first checks.
Have you tried another bank instead? From what I believe AdSense have only recently allowed Estonian sites, so I'm not sure if bank transfers are possible with them, but if not I would hope it will come soon. Give AdSense an email for alternative payment options, and if they don't have any available to you, maybe ask a different bank in your country if they accept cheques.
That means the bank does not want to do extra work dealing with checks. All you have to do is find another bank. Just go from one bank to another asking if they would accept that check and open account in one that accepts it. If none of local Estonian banks accept the check, then you try international banks like HSBC or Citibank.
Unfortunately, we don't have big international banks like HSBC here. But I will try my luck with other banks. Just don't feel like opening another bank account just for those adsense checks when I have been a happy customer of my old bank for 15 years now.