Facebook Messenger user privacy settings prevent one user from finding the 'exact' location of another user. However, there are a few ways you can find the city that a given user lives in.
If you are Facebook friends with someone on Facebook Messenger, go to their Facebook profile. Then click on the About tab and check their current city.
If you are not Facebook friends with someone, you might still be able to check out their current city (if their current city is listed on their public profile). (However, you won't be able to find a public profile for a user if they have set their privacy settings to hide their profile from the public).
Finally, you can do a quick Google search of the name of the Facebook Messenger user to see if they have any other public social media profiles. If you find another social media account for the user, it will often have their current city listed.