Help with Forms only for Admins

I am trying to find a way (either by plugin or simple php) to have a custom made form only for the Admins and have the information submitted to auto generate onto a page within our site.

We do restaurant reviews and I want to put in the contact info, location, etc. for each restaurant we review and have it show up in alphabetical order on a specific page.
This form can’t be viewable or usable by general readers but only by Admins.
Customization of the form would be nice too.

Is there a plugin out there that can be utilized for something like this?
Or is doing it through a plugin the best way? Is there a better way to do it?

Thank you for your help!