You don't have to live in the capital of Georgia (or Korea for that matter). Just a little outside the capital is already much more reasonable. You also don't have to maintain 100% "western" standard of living either, seeing that you aren't in the West. Very few people in Georgia make 1000+ euro, and they're doing OK with less. In rural Georgia you'd be living like royalty with that kind of monthly spend. It's also beautiful, and people are real nice. The only thing to watch out for is, of course, the internet.
If you're ok with Georgia, you should check out Batumi. It's a bustling coastal city that's seen impressive growth since independence. It's also pretty close to Turkey, so there are land routes to Trabzon (and flights from there to Istanbul).
Batumi is also known as Colchis, the destination for the Argonauts in Greek Mythology, so plenty of history & culture and great food.
The Grand Tour did a special driving through Georgia to Azerbaijan if you want to get a feel for what the region looks like:
