Method to implement price differentiation based on region selected by visitor

I have a simple wordpress website for a company that delivers services in different cities across the country. I would like visitors to be asked their region when they enter the website, and then when they go to the page with the price list, show the prices based on their region. Can anyone recommend a method to implement this? I looked at various plugins but I found none that seemed fit for the job. I could build a scheme with cookies etc. but my fluency in these things is limited and it seems like a common task, so I would expect an easier method to be available.

Thank you for any suggestions!