Havana Juice Rene Diaz at Havana Juice offers freshly pressed sugar cane juice – a natural, unprocessed option for anyone in need of a sweet treat. Squeezed directly from the stalk into your glass, sugar cane juice boasts a number of health benefits, one of which is a low glycemic index. Pair a glass with the stand’s famous Cuban sandwich made with ingredients from right here inside Market, and you’ve got yourself a delicious lunch.