Customize the form-portion of a view There might be a really simple answer for this, but I haven't found it yet.

I'm using a view with a few exposed filters.  The form it generates is too basic, and I want to restructure it a bit, with some "+ advanced" expanding/collapsing divs and things like that.

What method do I hook for this?  Or is there a better way?
You can override views-exposed-form.tpl.php template.
In this overrided template you can putup own div wrapper etc.
How to override any template(tpl) visit here.

You can also use hook_form_alter. It perform alterations before a form is rendered. So using this add some alteration on form.