Recently the request was made that a user, who had only contributor permissions, also be able to see the usage reports. I could see this coming up on several different occasions, after all, it isn’t uncommon to have a manager that will need to see who is using the site but is also someone that you won’t want them to be able to make design changes to the site. You can accomplish this using SharePoint Permissions. The following shows the site permission levels that are available and can be configured together to create custom SharePoint access.
The approach I recommend would be to create a new permission level called “View Usage Reports”. You could then create a SP Group set to that permission level and add whatever users needed to be in that group. Doing it this way gives you some flexibility and allows you to granularly add the ability for any level of user to also be able to view usage reports.
The screenshots below are from a user who is part of the Members Group and the View Site Usage Group. Even though they can see the site actions tab, the only things they see on the settings page are the usage reports.