I'm obsesses by this art piece I found while traveling and couldn't bring home.
What is this style called? How can I find more of it? Are there any digital tools that could help me generate pictures like this using pre-existing photos?
What is presented is a somewhat extreme manifestation of halftoning. Many graphics programs will allow halftone to be applied to an image. The extreme aspect is that the grid count is low, akin to a low resolution rendering. Other graphic attributes may have been applied prior to the final halftone application, perhaps posterizing and certainly grey scale but the final result is due to low resolution halftone.
I popped off a quick search for black and white image of Marilyn Monroe and found this website which provided this un-modified (but cropped and resized) image:
I use Paint Shop Pro™, but Adobe Photoshop™ is certainly going to be capable. Another search shows that GIMP is also capable of creating a halftone effect.
Changing the default dot shape from square to round and increasing the size to 4 in the parameters provided for the following result: