Kindly explain a bit more on what you are trying to achieve.

My Understandig:
1) You are having a site  of Publishing Template
2) You want to see the site from an end user perspective or anonymous user

My suggestions:
1) Enable Anonymous access to the site
Check the URL: technet.microsoft.com/en-us/library/cc263363.aspx
2) If you don't want anonymous access to the site, add the user to the vistors group. Login with that credential and check. If you login with the credential that has any higher access [like contributor / designer/ approver/ ..] you will be seeing the Site Actions


Kindly let me know if you have different Authoring and Publishing environment, i will provide my suggestion accordingly.

In the site  actions menu you can hide the page  editing toolbar. If you want to see the site without site actions you need to create a test user account in AD or a local user account and add it to SharePoint with reader rights only, then from the welcome menu, select sign in as a different user account and enter the test user's details.