By background images, do you mean things like this?
If so, I don't have all of them saved but I found them on Final Fantasy wikia. The pages for each individual location usually include an image of each section of the area. It would just require you to click down the list of locations in the game to open up the pages and save the images.
I have also found this resource (which the wiki sometimes draws from). They appear to have taken a screenshot of most, if not all, of the backgrounds for the whole game. However, I must warn you that they keep a watermark in the corner of all of the images, so that's something to bear in mind if you wish to use them elsewhere.
It might be safer to start with the wiki to see if they have a clean view of it.