Adittioniotal features to the Shipping Addres

Hello friends, i'm triying to findout how can i add adittional features to the shipping adress form.

The shipping will be done by my store employers in only one specific City, but whit different sectors of the city for exmple: (north side, east side, etc.), So some sectors of the city has additional shipping cost beacuse of the distance.
I will like to add a drop down menu at the shiiping addres info so customers can select the sector of the city, and that this selceted option deliver automatically the sector shipping cost to the total price... Examples:

North Side: No Shipping Cost
East Side: USD 5
South Side: USD 15

Thanks for your help...

Best Regards.