Create WooCommerce city selector

Hello, anybody may tell me the plugin or some modifictation of how to organize WooCommerce to work with different cities?

I have 4 cities, wher some products similar and someone the same but the prices is different, they have different locations and phones as well as manager which ones receive and manager the order are the same too.

I want user have ability choose a city (it saved on the coockie) and open always his city when he opening the site. But if he registred at one time, and moved to another city… he may choose another city with the same login info.

Thx