My mom visited Abkhazia several years ago when she was on vacations at Sochi. For Russian citizens it's easy but I don't know if it's even possible to visit for foreigners. She was there before at Soviet times and it's looks quite bad comparing to like it was looking before but mostly because of war in the beginning of 90s. Therea are still some war-torn buildings left. But it was about 5 years ago so I don't know how it looks like now. Btw I've spent my vacation this august in Crimea and it was beautiful. I strongly recommend to visit it, you will need a Russian visa for it though.