You haven't mentioned ...

the VERSION of Windows you are using if using Windows or your OS if using something else.

If using Windows ROBOCOPY can do just what you want if you familiarize yourself with its switches.

Read through this link and the links the thread points you to:
http://www.dslreports.com/forum/r20186464-Copy-a-folder-and-retain-the-creation-date

XP retains file dates if using the mir switch but not for the directories but if you run the same command again even the directory dates are correct.