How to make Web Services public

i created an android application that requires use of web service i want it to be able to access the app everywhere therefore i need my web services to be public with an external ip so i can access

what is the best way to do it? I have an Amazon Web Services account i dont know if created an instance and run the web services there will be the best solution My big problem with Amazon instance is that it takes a while to show in the app the result of the web service

Any ideas in how to make my web service public?