You could probably find something fairly cheap in the Baltics, outside of the capitals (Vilnius, Riga or Estonia). How you would go about doing this is more of a challenge. I have an idea that might work, which you could probably apply to any country (not just the Baltics), but since I'm most familiar with Lithuania, I'll use those terms.
I would contact the Tourism Office in Vilnius, which can suggest a travel agency which arranges for accommodations out in the countryside. Get in touch with them, and ask if they can suggest someplace for a month or so. If you were committing to a longish stay, they'd probably arrange quite a good rate. We rented a four room house for a week, for about $100, (for our family of 6), but for just one person, you could probably arrange to rent just a room for less than $100 a month, maybe a little more to get room and board. If you don't mind outhouses and living in close proximity with a non-English speaking family, in a small, isolated community, I think it would be quite possible to make such an arrangement - and what an incredible experience. I would suggest making the inquiry for a month, so that if you don't like it you don't feel compelled to stay, and also so they don't think you're planning to move there for good. If you like it, you can arrange to stay longer, or if you want to move on, you can do the same thing in another village or country.