Yes, Brazil requires visa applicants from the US to visit the consulate in person. They explicitly state that they do not accept applications by mail.
No visa applications will be accepted by mail.
When you finish filling out the electronic visa application form, print the application receipt, glue your picture on it, sign on the appropriate field and bring your application receipt form along with the other required documents to the Consulate.
The consulate serving Puerto Rico is in Miami, so it would require one visit to Miami. You would not be able to apply in New York or any other consulate. Fortunately you don't have to go back to Miami later to pick up your passport; the consulate will mail it to you if you leave a postage paid envelope with them.
In order to save you a second trip to Miami to pick up your passport, you may leave a prepaid self-addressed Priority Mail Express envelope from the USPS (United States Postal Service, the Post Office) for the return of your passport. The envelope must have a tracking number. The Consulate does not accept envelopes from other companies such as FEDEX, DHL or UPS.
