In Views admin, is there a section to insert CSS to style the view? i.e. how to style view without editing theme code or other drupal PHP?
While I agree that style rules belong in a CSS file (compare with PHP that gets Eval'd) I can see the requirement, especially if it was a multi domain site that ran different themes. You could write a custom module (basically what CSS Injector does as mentioned in a previous answer) but for a complete code free way you could use Panels which is much more aware of CSS, in that you can add some style rules to specific containers within the interface itself.
Actually, the latest views does allow all kinds of CSSing, both from the easiest, such as adding CSS classes to the view Style Settings section, to embedding custom css and fields wrappers in the fields output when you click on their configuration and edit Style Settings there.
But I think the question here is, after you do all that, where do you put the CSS itself.
And that would be in one of your theme's css files, which are defined in your themename.info file (which is located in your theme's toplevel directory) like:
stylesheets[all] = myfilename.css
So, you could ADD a css file to your theme with your customized CSS without touching anything else in there.
Views does not have anything like that because it belongs in a theme. It's considered good practice for module maintainers to keep themeing small and out of the module itself.
The closest you can get to not editing theme CSS or template pages is using the CSS Injector module.