Summarize:

Go to https://www.facebook.com/. This will open your Facebook News Feed if you're logged in. If you aren't logged in, enter your email address (or phone number) and password in the top-right side of the page. This field is at the top of the Facebook page. Type in the name of the person you want to find, then press ↵ Enter. Doing so brings up a list of people in your area with a matching (or similar) name. It's just below the search bar at the top of the Facebook page. You'll find this link on the left side of the page beneath the "City" heading. Clicking it opens a search bar. You'll see suggestions appear below the search bar as you type. It should be below the search bar. This will refresh the search results to display people who have both the name and the city you selected on their profile. For example: if you typed in "Sarah Smith" as the name and selected New York as the city, you would see a list of people named Sarah Smith who live in New York displayed here.
Open Facebook. Click the search bar. Enter a person's name. Click the People tab. Click the Choose a city link. Type in a city's name. Click a city's name.