Is there a CSS way to add an arrow if a ul has a ul child?

This is perfectly doable in CSS —

Your structure is this:

 <ul class="menu">
      <li>
           <a href="#">Has arrow</a>
           <ul><li><a href="#"></a></li></ul>
      </li>
      <li>
           <a href="#">Has no arrow</a>
      </li>
  </ul>

Your CSS will be like this —

   //this adds an arrow to every link
  .menu li > a:after { content: '>'; } 

  // this removes the arrow when the link is the only child
  .menu li > a:only-child:after { content: ''; }   

Taking it one step farther, if you want to have a drop down menu where there is a down arrow on the top level items and then right arrows for sub menus, your CSS would look like this

   // set up the right arrows first
   .menu li > a:after { content: '>'; }

   //set up the downward arrow for top level items
   .menu > li > a:after {content: 'v'; }

   //clear the content if a is only child
   .menu li > a:only-child:after {content: ''; }

Here is a jsfiddle of it in action – http://jsfiddle.net/w9xnv/2/