I would definitely recommend Tbilisi, the capital of Georgia! Great wine, great food and beautiful mountains. 2 days eating and drinking there would be a blast. I was there a couple years ago for work and loved it.
oneworld.com lists Tbilisi as a destination. Flights are BA7566/5 but they're operated by BMI so I'm not sure if they are eligible for whatever fare you're booking. So its only a oneworld codeshare city, not on oneworld metal. But it would be fun nonetheless!