Abkhazia is not a tourist destination in any normal sense. Entry is closed from the Georgian side and treated as illegal entry into occupied territory; entry from Russia exposes you to Georgian criminal charges should you ever return. The list below describes the main sights for completeness — they sit empty of foreign visitors and will likely remain so.
The capital Sukhumi, the lake at Ritsa, the cave system at New Athos and the Black Sea coastline together formed one of the most prized resort regions of the Soviet Union. Today the infrastructure is either decaying or being slowly rebuilt for Russian visitors. The historic Greek and Byzantine sites along the coast — early monasteries, fortress ruins, a string of Black Sea harbours — date back two thousand years and predate every modern political claim on the land.