when visitor open shop 1st time give him ability to choose his own city
when visitor see name of his own city at page header - this give more trust to shop, becouse visitor understand that no problem with delivery to his city
also its good to shop owner - he can choose only cities were he work or where he have stores
example - http://www.ulmart.ru/
We have two add-ons that allow to determine customer's geolocation: IP Geolocation by MaxMind (https://www.simtechdev.com/addons/customer-experience/geolocation-by-maxmind.html) and Geolocation by Google (https://www.simtechdev.com/addons/customer-experience/geolocation-by-google.html)
also actual when shop set different prices for different cities !
and after user choose his city on mane page, when he make registration, name of his city alredy in registration form