Build something that works
Thanks Alex that link you posted has almost got me there but getting a strange error when not using www. will chat to the domain provider.
This is the Heroku article you should read to see how to set it up (for all hosting sites, not just GoDaddy): https://devcenter.heroku.com/articles/custom-domains
For the basic setup, follow the section for Custom Subdomains. The rest of the article focuses on advanced setup, like getting not just www.example.com but also example.com (called a root domain).
Thanks Gemma. I would also suggest using DNSimple for hosting, if you still have the flexibility. While GoDaddy is fine (and may even be a little cheaper), DNSimple is really easy to navigate and I find that the time/frustration you'll save is well worth the extra few dollars.
I also found a good explanation of how to set up your domain for GoDaddy specifically: http://jgallardo.me/how-to-point-a-domain-from-godaddy-to-heroku/