How do I get a date in YYYY-MM-DD format?

Just use the built-in .toISOString() method like so: toISOString().split('T')[0]. Simple, clean and all in a single line.

var date = (new Date()).toISOString().split('T')[0];
document.getElementById('date').innerHTML = date;

<div id="date"></div>

Please note that the timezone of the formatted string is UTC rather than local time.