We announced, back in January that new Google Sites did not support URL mapping for custom URLs. We heard that this is a very important feature for many of you and provided feedback to Google.
Thank you for your patience! Google listened to our feedback and recently announced that custom URL mapping has been added to the new Google Sites. Now you can have a friendlier, easier-to-remember, URL for your new Google sites.
Find out how to request a Custom URL for Google Sites.