You or Yourself?

Solution 1:

Yourself is a reflexive pronoun.

Examples

Look at yourself!

You always compare yourself to others.

In other words it is normally the object of a verb and usually refers to something you do to yourself.

The difference comes when the action is done by a different person, e.g.

You would not say to someone, "I need a word with yourself." (not in standard English anyway)

Therefore in standard English you say:

What is a nice, smart girl like you hanging around a group of kids like them for?

However in some versions of English that 'rule' is not true. In Ireland for example it is very common to hear something like "How's yourself?" in place of "How are you?" or even "I need a word with yourself."

So, it's a judgement call and it depends whether you are Irish or not!

EDIT

I just noticed that the answer is in your sentence.

What is a nice, smart girl like you hanging around a group of kids like them for?

versus

What is a nice, smart girl like yourself hanging around a group of kids like themselves for?

All you have to do is be consistent. Which version do you choose?