All perfect praise be to Allaah, the Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
After narrating the story of Ibn ‘Abbaas’s refusal to adopt the vision of the crescent made by Mu‘aawiyah both, At-Tirmithi commented saying, “This opinion is adopted by the senior scholars. They see that each locality has its own vision as long as they have different moonrises; namely, the crescent may appear in a country but does not appear in another.”
Consequently, if the crescent was seen according to the Sharee‘ah-approved way in the neighboring cities and their moonrise was the same as yours (which is most likely the case), then your city must follow them. In such a case, you have to start the fast with the neighboring cities.
If the moonrise in these cities is different from the moonrise in your city, then the people in your city are not required to fast according to the vision of the moonrise in the other cities.
However, there is no harm if you chose to start the fast with the neighboring cities and adopt the opinion of the scholars who said that seeing the crescent in one country would then apply to all countries, because this is a matter of Ijtihaad (personal effort in reaching a ruling).
In short, the opinion of the majority of scholars is that if the crescent appears in a land or location, then all its people must fast or break the fast. Nevertheless, if you fear that this may cause Fitnah (discord), then you should fast secretly.
Allaah knows best.