Speaking as a health professional who likes juice, I don't assume I'm getting any significant health benefits at all and that the health consequences of drinking fruit juice are about the same as drinking sugar water. Tastes a lot better, though.
That said, I get fresh orange, grapefruit, and lime juices at La Sirenita several times a week, and coconut water and non-citrus (carrot, beet, etc.) juices occasionally. There are several other good places (particularly at the Mercado Municipal or a stand at Calle 11 and 10 Av) but their hours are less predictable and La Sirenita is by my bank and barber. If you're staying near La Choza, head north on 10 Av to Calle Dr. Adolfo Rosado Salas, turn right and go 2 blocks to the Mercado Municipal (which is between 20 and 25 Av) where there are lots of cool little shops including a greengrocer that sells juices. There's parking there and that's where we get guayaberas, molcajetes, and birdcages, so that's where most of our juice comes from apart from La Sirenita.