You can conditionally display the sub navigation and/or any surrounding HTML using the following parameters with nav_sub:
{if structure:child_ids != ''}
<div id="sweet_nav_wrapper">
{exp:structure:nav start_from="/{segment_1}"}
</div>
{/if}
Additionally, you can show alternate markup or content using if:else as follows:
{if structure:child_ids != ''}
<div id="sweet_nav_wrapper">
{exp:structure:nav start_from="/{segment_1}"}
</div>
{if:else}
No children!
{/if}