If you haven't found it already - set the "Save" dialogue to show more info. Maybe this is what you are referring to.
Open up any application (Text Edit, eg)
Click to "Save As" to bring up the dialogue.
Do you see that little triangle to the right of the name of file field? Click it.
Either the dialogue box expanded - now you can save files with more control (note the Create New Folder option, bottom left). Or the dialogue contracted, so click the triangle to restore it.
I pretty sure that this change is saved system-wide. And hopefully helps to solve your problem. Note that there is a similar triangle when you print, and the expanded dialogue is actually useful.
If you are using iPhoto, Aperture, or Lightroom you don't need to organize your images - the application does it. And, imho, you should be using keywords instead of dates to find those images. There are some good threads here on that topic.... just go searching for them.
If you aren't using iP/Ap/Lr - why not? I think iPhoto still comes free, and Aperture off of the App Store is way cheap.
Hope this helps.... if not, we'll need some more detail because I don't think we understand what the problem is.