If you actually used a Mac back in the late 80's / early 90's, this site's output will give you a heady shot of pure, undiluted nostalgia. I wasted half an afternoon once, converting images for my imaginary Hypercard project.
Photoshop will also give you options and allow you to reduce colors down to an 8 bit or 4 bit palette, with a variety of dithering choices, or for the true lofi look (It's 1991 and I used the school's lab scanner for the first time!), no dithering at all.
If you happen to be writing your simulated vintage mac site on a modern mac, vImage (part of the Accelerate framework) supports Atkinson dithering from OS X 10.9 onward via vImageConvert_Planar8to[Planar|Indexed][124].
Not overly useful for one image, but if you have lots of them, it's nice to have a programmatic solution.
I was having a shit day, but now it's awesome. Thank you!
P.S. I will go build like 9 websites using this immediately.