If you want to be able to add unlimited names and cities to a database, then make a component.
If you want just two text fields, then make a module.
Plugins are more for filtering content once it has been added to the site, so do not seem applicable here.
If your template is a bespoke one, then you may also have the option to add template parameters if these fields are to be site-wide.
Joomla's documentation is as good as anything - it doesn't sound like you need anything beyond a basic hello world module to do everything you need. Modules are far simpler than components.
If you browse around, there are a few module creators that may do what you want, but if you have the PHP knowledge, modules aren't that tricky.
I'm not quite sure what you mean by "want this functionality only in admin panel not in the front end". Generally you'd add the content in the back end and display it in the front end. You may wish to edit your question to explain what you want to do with the information once someone has entered it, if it is not to be displayed on the front end.