Riv, I have at last found a direct reference to wines in none other than
The Hobbit. From the chapter "Barrels Out of Bound:"
It must be potent wine to make a Wood-elf drowsy; but this wine, it would seem, was the heady vintage of the great gardens of Dorwinion, not meant for his soldiers or his servants, but for the king's feasts only, and for smaller bowls not for the butler's great flagons.
According to Karen Wynn Fonstad's
The Atlas of Middle-Earth, Dorwinion is "The Land of Wines." You can find it on her maps on pages 53 and 77. located in the area where the River Running terminates into the Sea of Rhun.
According to The Encyclopedia of Arda, Dorwinion is "A little-known land, probably lying in the vales of the River Running, famed for its great gardens and the quality of its wine."
While Dorwinion might be the producer of the finest wines in Middle-earth, that does not mean it is the SOLE place that produces wine. Therefore, since Tolkien apparently associates vineyards with gardens, it might also be feasible to assume that Ithilien, the "Garden of Gondor," would be a location that would feature vineyards. Lebinnin might also be a good possibility because of its many rivers and fertile soil.
Elsewhere, I strongly suspect that the Shire produces its own wines, as well as the garden/orchard areas in Rohan. The entire area around Laketown and Dale was described as turning into a teaming garden after the death of Smaug, so I suspect they had vineyards. The elves surely produced wines -- as well as miruvor -- in Rivendell and Lothlorien.
Hope that's helpful!