I have an URL for the site but not for it's feed(s), which I want to parse.
How to detect if site has an RSS/Atom feed(s)?
As mentioned in this question How to check if a site has rss feeds you need to download the page and check for a rel='alternate'.
You could also have a fallback to regex the page for any mention of a feed.xml or similar, should the first parse fail, if you want to be sure to find any possible link to a RSS/Atom. This would not be as certain to contain the RSS of the actual page, it could be a link to an outside RSS.
Look for the rel="alternate" type="application/rss+xml" link in the head section of the site's defalut page:
<head>
<meta http-equiv="Content-Type" content="text/html; charset=windows-1252">
<link rel="alternate" type="application/rss+xml" title="RSS 2.0" href="http://someurl/feed/" />
<title>Some title</title>
</head>