Is The New York Times a Credible website?

Yes, its news site is generally both accurate and credible, although there have been occasions when the Times got the story wrong (reporters are human; they can make a mistake sometimes). But for the most part, New York Times reporters are well-respected and the website is very thorough about covering all aspects of current events. On the other hand, the editorial and opinion pages of the Times tend to lean liberal/progressive; there are some conservative writers, but the majority of the opinion writers lean center-left.