Shipping method without Zip code

Hello! I´m setting up an e-shop shipping methods and so far have discovered woocommerce default option to insert areas for different flat rates. Therefore the client inserts address and zip code and system calculates the shipping cost. Since finding out the zip code often requires going to some other site to find the number, then client doesn´t want to do it. I´d like to get rid of zip code logic and do it so that client sees options written in text (example: Option 1: New York, Washington 5 dollars, Option 2: LA, San Francisco 10 dollars; etc). Client chooses option with tickmark and system calculates the rate accordingly. Later client has to also fill the address fields, but the shipping cost would not be affected by this. This is only for the courier to know exactly where to deliver the pack.

Example: https://kalamajakaktus.ee/

The page I need help with: [log in to see the link]