It's extremely unlikely that you'll be able to find a cached version of any page on nytimes.com. The web page authors specifically request that search engines do not cache their pages by using the following tag in the source code:
You can also use the cache: search operator. For example, searching for cache:en.wikipedia.org will show Google's cached version of the English Wikipedia page. As mentioned above, not all pages are cached by Google.
I made a site, viewcached.com , which aims to make it easy to use the caches from Google, Yahoo, Bing, Wayback Machine, and Coral CDN as mentioned above, and in addition, Gigablast and WebCite. Hope this is helpful.