Our oldest archaeological evidence of human alcohol production dates to 7000 to 5800 BC. The location is Jiahu China. It might be a stretch to call this wine because it contained rice and honey but it also contained tartaric acid which is is very rare and mostly found in grapes. Tartaric acid can also be found in a few other local fruits but grapes seems probable since they are a great vector for fermentation yeast.

If you are looking for "pure" wine our oldest indirect evidence are grape seeds found in Turkey that date back to 7200 BC and this area has the wild grape plant. There are even older grape seed finds such as those found in Burgundy France that date to 14,000 to 12,000 BC but these were clearly gathered and not cultivated in both cases there is no direct evidence for wine.

The oldest clear direct evidence of wine production is from what is now the republic of Georgia and dates to 6000 BC. Tartaric acid is found in in broken jars. A bit after this era (5600 BC) you can find wine evidence in the mountains of Iran.