Abkhazia is a de-facto independent state on the eastern coast of the Black Sea and the south-western flank of the Caucasus.
Hitchhiking in Abkhazia is definitely easy. Be aware that off the main road, especially in the southern districts, traffic can get very sparse.
Abkhaz drivers love to drive very fast, be aware of that and get out whenever you're afraid of crashing into roaming cows or horses along the way. Abkhaz police is very friendly in general, don't be afraid to hitchhike next to their police posts. Nevertheless, hitchhiking is possible everywhere, even inside Sukhum, and you won't wait longer than a minute or two at all.