Is there a good way to attach JavaScript objects to HTML elements?

Have you looked at the jQuery data() method? You can assign complex objects to the element if you want or you can leverage that method to hold a reference to an object (or some other data) at the very least.

JavaScript objects can have arbitrary properties assigned to them, there's nothing special you have to do to allow it. This includes DOM elements; although this behaviour is not part of the DOM standard, it has been the case going back to the very first versions of JavaScript and is totally reliable.

var div= document.getElementById('nav');
div.potato= ['lemons', 3];