"I need to go to the Ministry of Internal Affairs because I lost my passport."
Translation:אני צריך ללכת למשרד הפנים כי איבדתי את הדרכון.
The Ministry of Internal Affairs office in Jerusalem is located on Shlomtzion Hamalkah Street, a short distance away from the Jerusalem Municipality and the stop in front of it on the light rail. They have times when they are open to the public, and other times when you can only enter if you have an appointment. I had to go there a few times for my student visa when I was in Israel this past school year (2015-16)
There's a branch of the Ministry of Internal Affairs in every major city in Israel. If someone lives in Haifa they don't need to go to Jerusalem to get a passport.
Passport = דרכון Dragon = דרקון You're right that it should be הדרכון שלי, but the sentence is correct without it as well. The ownership of the passport is implied.