Я бы пошел с .closest()
с селектором
$('span').closest('.foo').length > 0
console.info('span has foo?',
$('span').closest('.foo').length > 0)
console.info('span has bar?',
$('span').closest('.bar').length > 0)
console.info('span has baz?',
$('span').closest('.baz').length > 0)
console.info('span has whatever?',
$('span').closest('.whatever').length > 0)
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>
<main class="baz">
<div class="foo">
<span class="bar">Hello</span>
</div>
</main>