I have just finished developing a REST web service that is consumed by a mobile application. The web service is developed with Java and runs on an Apache server.
Like I said, if it is for testing purposes you could always use a "normal" PC, running something like XAMPP.
As an alternative you could give RedHat's OpenShift a try, which offers a free, getting-started plan (more info here) that should more than cover your testing requirements.