Is it best to save an Adobe Illustrator file as a PNG, then opening the PNG and saving it as a JPEG, before converting it to a PDF file? I've noticed PNG files look blurry and pixelated when converted to a PDF file.
I don't know why you would ever want to export as a PNG, convert to JPG, then save as a PDF. Any time you save as a JPG, you are going to lose quality. There is a reason that AI lets you save files directly as a PDF.
The image quality will also be greatly affected by the compression settings that you choose in the Save Adobe PDF options that will pop up.
If file size is not an issue (printing, for example) then I typically set it up as follows:
You can adjust the compression to suit your needs, if file size is an issue.