Are you sure you did not mean to take a left at TiPb and post this question there and even better yet... How come a Forum Mod has not moved this or even taken it off?
I have a good solution for you to Sync iPhone Contents to new Mac. You have to connect your iPhone to Mac , Now open a library to choose files you want to back up to Mac, Then the program will transfer the files from iPhone to Mac.
Log-in in to your iTunes account on your new Mac and then sync as normal. You'll be asked if you want to copy stuff from your iPhone to Mac (which you probably want to do) and then you should be able to continue as normal. Remember to authorize your new Mac with your iTunes account as well.
Besides there is a step by step instruction on how to transfer or backup iPhone contents to Mac.
Hope it can do you a favor.