The second 'to' means the same thing as 'in order to':
"Where am I supposed to go (in order) to send my gift to you?"
The second 'to' does not tell you "to a place" or "to someone". It tells you about the means of way of sending the gift.
You might reword the sentence this way:
"Where am I supposed to go so that I can send my gift to you?"
- For Teachers