Save for the web and device is exactly that not the right way to go about this, if you need 300 ppi, not 300 dpi.
and 1200 x 1200 pixels is 1200 x 1200 pixels so 300 ppi in this relationship is a a dimensions matter.
so a 1200 x 1200 pixel document at 300 ppi is 4 inches x 4 inches.
So what you want to do is to export (File>Export>Jpeg or PNG) it as a jpeg ore png but 300 ppi suggest that your final destination is print and not the web.
If you are sending it to print you want cmyk as your color mode and save for the web will make it rgb.
If you are saving to use on the web then you want 72 ppi anyway and save for the web is correct.
To make it export as 4 x4 @ 300ppi use the export way.
BTW for print you really should export as tiff.
for Power Point do export as jpeg or png.
...I usually start off with a new canvas of 1200x1200 px in 300 DPI...
No, I'm sorry, but you don't. Not in Illustrator. This statement reveals the basic misunderstanding you are stumbling over.
There is no "canvas" in Illustrator in the sense of a program like Photoshop, in which you open a "blank" document of a certain number of pixels, with each pixel just initially being white.
There are no pixels when you create a new Illustrator document. There is just a literally empty document. No pixels, no nothing. It contains no pixels at all, even if you have the rulers set to its ridiculous selection of "pixels." (You'll know why this is ridiculous in a few minutes.)
An Illustrator file contains objects, not pixels. Those objects can be of several different types. One type of object an Illustrator file can contain is a raster image, and raster images, of course, contain pixels. But until there is a raster image on the page, there are no pixels at all. And even when there is a raster image on the page, its scale (PPI) has absolutely nothing to do with the "pixels" of the page rulers.
When you export an Illustrator file as a single raster image--using either the Export dialog or the Save For Web & Devices dialog--that's when you create pixels. In fact, if there are already any pixels on the page (in raster images), those pixels are going to be resampled to new pixels to become part of the one big raster image you export.
Consider: Each raster object on the page in Illustrator is independent. Each one can have a different scale (PPI). So even if your document sizes is ridiculously called "1200 pixels x 1200 pixels", it is not. Consider this example and then tell me how it could be:
Suppose you have drawn a 4" x 4" rectangle on the empty page. You have then rasterized the rectangle at 300 ppi. Clearly, the raster image now contains 1200 x 1200 pixels. But the page rulers say it measures 288 pixels on a side. How can that be? Read on.
so a 1200 x 1200 pixel document at 300 ppi is 4 inches x 4 inches.
In Illustrator, this is absolutely not true. A 1200 x 1200 "pixel" document in Illustrator is certainly not 4 inches by 4 inches. It is 16.666 x 16.666 inches. This is because of one simple fact: The "pixels" referred to by Illustrator in its Document Setup dialog and in its rulers are not pixels at all. They are points (1/72 inch).
If you don't believe that, do this simple exercise:
Create a new document in your customary way, 1200 x 1200 with Pixels as the unit. Now stop here for just a moment, and look in that document setup dialog for where you tell Illustrator what PPI you want the 1200 x 1200 document to be. Can't find it. It's not there. There is no PPI in an Illustrator document, so you cannot say a 1200 x 1200 pixel Illustrator document is 300 ppi. (If it's anything, it's 72 ppi, but even that is skewed logic.)
Now rightClick the ruler and change the unit to inches. How big is the document?
Look at the 1" mark on the ruler. Change the ruler back to Pixels. How many "pixels" are converted to an inch? Keep doing this. Use any trick you can find in Illustrator to make its rulers convert an inch to anything other than 72 "pixels."
Now answer this: How big is a pixel?
You can't answer that question because a pixel can be any size you want it to be. It's like asking 'how big is a space?' The very fact that you can scale an image to any ppi you want (make it 1200 ppi or 12 ppi, without adding or destroying any pixels) prooves that a pixel has no fixed measure. And that's why it's ridiculous for a program like Illustrator to use "pixels" as an absolute distance measure in its rulers the same way it used inches or centimeters. It's pure nonsense.
If a pixel has no fixed measure, then how in the world can you use it as a unit of measure on a ruler? You can't; not legitimately, not in the sense of measuring dimensions of objects or pages. (Remember? Illustrator handles objects. Illustrator's rulers tell you the size of the objects.) Anywhere on that page, there may be a 1200 x 1200 pixel raster image, somehow occupying 72 "pixels" or 3000 "pixels" or 150 "pixels" of your page. Used as it is in Illustrator's rulers, "pixels" is nonsense.
Illustrator's "pixel" rulers are a complete sham. You can put a 1200 x 1200 pixel image on an Illustrator page and make it "measure" any number of sham "pixels" according to Illusrator's rulers you want. Therein lies the answer to your question:
Forget about Illustrator's rulers as being a count of pixels. It is not. It's a measure of 1/72" units (in other words, points). Do not think of the sham "pixels" on the ruler as being pixels. Think of them as being what they are: points. Then your confusion will begin to clear.
Better yet, don't use sham "pixels" as your ruler units at all. You want a 1200 x 1200 pixel raster image exported from Illustrator at a scale of 300 ppi, right?
You've been told you can't do that using the Save For Web & Devices dialog. If you've read and understood the above, you should now know that is not true. You would of course use the Export dialog to create a raster image that embeds a scale factor other than 72 PPI in the image file, because the Save for Web & Devices dialog assumes a browser which ignores the scale factor embedded in a raster image file. But for the sake of understanding, let's use Save For Web & Devices anyway:
- Forget about Illustrator's sham rulers. Create your document the size you know you want it to be: 4 inches x 4 inches.
- Create your artwork on the page. You can use raster images, text objects, vector objects, or any combination of those.
- Now you want a 300 PPI raster export of your whole 4" x 4" page. Third grade math tells us that will require 1200 x 1200 pixels.
- File>Save For Web & Devices. The Save for Web & Devices dialog opens. Select the raster file type you want, either JPEG or PNG. Go to the Image Size tab. What do you see? Original Size and settings for New Size. Original Size is 288 x 288 pixels (See? Illustrator unyieldingly considers a pixel on its rulers to mean 1/72 inch). But you can enter 1200 x 1200 (or any other desired pixel count). Click Apply.
- Save. Select Images Only.
- Launch InDesign. Import the image. Note the size. (Does 16.666 ring a bell?) In the Scale X Percentage field, key "4 in". (That's right, key an absolute value into the percentage field.)
You now have a 1200 x 1200, 300ppi image. You did it using the Save For Web & Devices dialog. And you didn't even use Illustrator's ridiculous "pixel" rulers.