Unique icons next to each WordPress menu item

You can probably do this with an icon font, like FontAwesome, plus CSS, in your theme’s style.css file (hopefully using a child theme). Each menu item is usually a list item in the HTML, and usually they each have a unique class and/or id, so you can use that to target each one. Add the ::before selector to insert your icon before the list item, something like this:

li.class::before {
    font-family: FontAwesome;
    color: #43CC9E;
    content: "\f06c"; /* escaped unicode for the icon */
    float: left;
    width: 1.6em; /* icon width + space */
}

Here is a CodePen I made, where you can play with the HTML & CSS using FontAwesome to place icons before list items this way.

This article tells you how to get FontAwesome into your WordPress site, and a lot more info about how to use it. There are, of course, other icon fonts, and the principles are the same.

On the FontAwesome.io website you can see each icon and get the unicode for each.