If you go to View -> Modify this View, you can select from the fields you'd like to have visible in the default view. There should be several options for some fields, and the one you likely have by default will be something like medium city (linked to document with edit menu). Choose medium city on its own and you should be good to go!
I solved the problem.
The source list "Cities" had three columns - "Name of the city", "Name of the city (linked to item)" and "Name of the city (linked to item with edit menu)".
When I was creating the "medium city" column in the "Customers" list, I chose "Name of the city" from the drop-down list. I was positive it was the 1st column but it turned out it was the 3rd one.
I modified the code filling the drop-down list with data so it contains no linked to item columns and it's working fine now.