First, you need to enable the Shape Tracing feature. It adds a toolbar at the bottom of the page, which can be used to explore all the template components of the page so you can see exactly which "shapes" are responsible for rendering different parts of
Now, that published date/time is a bit weird in how it renders, because its actually happening from code. You can still override the template tho.
In Parts.Common.Metadata there isn't a string relating to the date. What's happening is that it chains into rendering another shape called "PublishedState" - and it's passing in the created and published dates from the dynamic model. They're
DateTimes, not Strings ;)
The PublishedState shape is defined in Orchard.Core\Common\Shapes.cs - it's a method that generates a template from code. But if you create your own template called PublishedState.cshtml and add it to your theme, it'll override the core shape.