How to access iPhone backup through computer after setting up as new?

So, I had to wipe my iPhone clean and set it up as new (as recommended by my local Genius Bar) because I was having issues with text messages (not iMessages) and voicemails. It seems like the issue is gone, but I now realized that I had some stuff from my backup that I want on my new phone.

Is there a way to access the photos/videos, etc in that old backup through iTunes without having to actually put it on a device?