This is an often-asked question and the simple answer is that you cannot change the 72 DPI that PS embeds in its Save for Web images.
The workaround is to use other PS controls so resize and save the image without using Save for Web and just use Save As.
Can I ask why you need to use Save for Web and why you need a PPI/DPI different than 72dpi?
You go by pixel dimensions for the web because that's all that computer screens use.
dpi or rather ppi is a print specification.
In this example, Image > Image Size I have unchecked resampling and set the ppi to 300. You can see how small it's going to print on paper as opposed to maybe 100 ppi. It will still retain the same pixel dimensions.
You basically focus on a good pixel size for the the browser display.
Thanks everyone! I was able to save as needed. Much appreciated!