Simple modification for menu structure

I’m trying to make a menu for my website, but I want it to be easily modified through original WP menu(dashboard > appearance > menus).
I want to add some small thing to the structure of my menu, originally it goes like this:

<ul>
    <li>something goes here by default</li>
    <ul>
    <li>something goes here by default</li>
    </ul>
    <li>something goes here by default</li>
    </ul>

So, what I want is that between the ul and li tags will be some my code, for example:

<ul>
    <mytag></mytag>
    <li>something goes here by default</li>
    <ul>
    <mytag></mytag>
    <li>something goes here by default</li>
    </ul>
    <li>something goes here by default</li>
    </ul>

I know I should make some changes to functions file, but I don’t know how to do so, can you please help me a little bit?