Changing email addresses on my @me.com and @icloud.com
Unfortunately, as was stated, you cannot change your @me.com or @icloud.com email addresses independently of your Apple ID. What I would recommend doing is setting up a Gmail (or other) address and using that as your primary Apple ID email (as well as all your normal email for that matter).

If you have a Mac you can even move all the email from your @icloud.com/@me.com account to your new Gmail account simply by setting up both and dragging the folders from one mail account to the other. 

After you set up a Gmail email address you can edit your Apple ID preferences at this site. That way, all you ever basically see is the new Gmail account.