For a simple site that doesn't get too much traffic, Heroku hosting is pretty cheap. At the time of writing this, most small sites can run on a single hobby-level dyno for $7/month.
If you want to be as cheap as possible, you can try the free level, but your site will "go to sleep" after 30 minutes of inactivity. After that happens, the next time someone tries to visit the site, it will take a longer than usual to respond while "wakes up".
Check out Heroku's pricing page for current information.