A very simple and quick method to find the current local time in any city or country is via search engines - just type time in [City or State or Country Name] in your favorite search engine or even inside the Firefox search bar to instantly know the local time of any global location.
While Google, Yahoo and Ask.com support the time search syntax, Yahoo and Ask seem to have better algorithms than Google and they also support a wider set of cities.
For instance, a query like "Time in USA" or "Time in Russia" would return no results in Google since these countries has multiple timezones. However, Yahoo and Ask.com would return the current local time of their capital cities which is an intelligent approach.
Ask.com is even better since it offers suggestions for related cities in other states or if a city with the same name exists in different states or countries. [for instance, Washington is in US as well as England]
Ask.com also supports zip code of US cities. So a query to find the local time in Manhattan, NY would be "what time is it in 10005". Great time saver.
Related: Convert Currency Online using Search [Thanks, Karmadude]