Is there a way to see the time that a photo was taken on the iPhone? Sometimes I took a photo using my iPhone, and then later on, I wonder how long I have been there at that location, I thought of checking when the last photo was taken, and can tell the time when I arrived, but I found it wasn't easily possible to see what time the photo was taken.

Is there really a way to see the time that photo was taken, be it 1 hour and 20 minutes ago, without using any third party app and without importing the photo to a computer?  I thought this might be a simple photo info thing that might be invoked by some easy way?
You are not missing anything, the iPhone has no mechanism to see that information natively. However, if you search for EXIF on the App Store, there are a few (some free) apps that will happily do that in the device itself. 

You must note that, due to the way iTunes work, pictures coming from iTunes will not have their metadata associated. Sad but true.