I am based in Europe and I would like to test my website as if I am located in New York. I have some specific features that will be visible based on cities.
You have a few solid options that will return results in Google and display the site as you were actually in their country. The most common methods are Proxies and VPN (Virtual Private Network) This are available as free or paid, paid services tend to be fast and not very noticeable your using a server to connect to the desired site. While a Free Service is normally painfully slow at times and especially noticeable when downloading or watching videos on such sites as YouTube.
VPN VS PROXIES
I won't go into every plus and negative about both but what you should know is that VPN tends to be much more secure than proxies due to encryption and the authentication system works.
There are a few free proxies and vpn's such as Zend2 and VPN Book.
Based on how you implemented it you could set up a local proxy (or even re-configure your local webserver) to explicitely send X_FORWARDED_FOR headers with specific IPs related to NY.
There's are VPN's you can use. HMA VPN and Overplay are a couple you could get for like 10 bucks per month.
There's a lot of applicable resources to test this without the need of installing a proxy, VPN or something else, like Webpagetest.org, slow but working with good information.