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?
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.