You can apply for both the DNI and the passport at the nearest consulate to your residence in the U.S. or in Argentina, depending on how long you plan to stay and where you are located. If you choose to do it in Argentina, it’s advisable to make an appointment and bring all your documents. You’ll need to enter with your U.S. passport and then complete the process there. If you decide to handle it in the U.S., make sure to go to the consulate that corresponds to your residency, not just any consulate. It’s a good idea to call or email to inquire. Generally, you will need to fill out some forms and provide certain requirements, and the processing time can take at least a month since it is issued in Argentina.