In my GWT application, on the client side Java file, I have written a line to print the Locale:
System.out.println(Locale.getDefault());
In addition to information in RAS's answer, you could use GWT's class LocaleInfo to obtain information about available locales or current locale.
System.out.println(LocaleInfo.getCurrentLocale());
Hope this helps!
The client-side of GWT does not have access to the whole Java API. Java.util.Locale is one of them. You can't use or even import it on the client-side. But you can definitely use it on the server-side of GWT. You can find the list of classes that can be used at client-side here.