A server app isn't very useful without a server!
Luckily, Heroku provides free plans for limited use and is super easy to deploy to. At the moment, they allow 18 hours of uptime per day on the free plan, with your machine downcycling when it isn't active (in effect, this means that your server generally won't ever run out of uptime hours provided it isn't being hit with traffic constantly).
Start by creating an account at http://www.heroku.com and install the Heroku Toolbelt from http://toolbelt.heroku.com. Once you've done so, go to the root of your project folder and type the following:
$ heroku create
This will create a new Git remote and set up your app at a random URL, like https://calm-dusk-16214.herokuapp.com/.
Next, create ...