Need advice on multiple locations implementation

CMS & WordPress
1

I would like to have a menu on my top bar where users select their Location - let’s say for now: London, Paris, Rome

I have a custom field on each post which takes the value London, Paris, Rome.

When the user selects a category and his chosen location is London - I only want to show him the London posts…

Questions

  1. How do I implement the functionality where they get to choose their location ?

  2. How do I filter the posts in each category?

Any ideas would be much appreciated. Code is more than welcome too and I will test this and provide feedback.

thanks
Andy