The United States Citizenship and Immigration Services (USCIS) has branches and offices throughout the country, including local offices, application support centers, and service centers. USCIS also has operations in many international locations. Here is a Google map that shows all USCIS locations around the world.
USCIS provides an excellent Office Locator on their website, where you can search for a particular office by Zip Code or State. The only tricky part is that for a new immigrant, the differences among various types of offices are not obvious. For example, you want to look for an application support center (ASC) for fingerprinting needs, but a field office for customer support, even though they may be located in the same city.
Below is a list of most USCIS offices, including headquarters, field offices, service centers and international locations, but excluding application support centers and other specialized offices. They are color coded to separate them into different groups by function.