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 550 (plus an additional 450 if you verify your account with a credit card) dyno hours distributed between all of your servers, with machines down cycling when they aren'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 a new file named Procfile...
