The word “nite” is an informal, simplified spelling of “night,” which, of course, is formally defined as “the time from dusk to dawn when no sunlight is visible.” As such, I wouldn’t recommend the use of “nite” in formal school essays or college dissertations; that surely would invite derisive underscoring or provoke a dismissive question mark from your professor. In less restrictive situations like postings on Facebook or Twitter, though, using “nite” instead of “night” definitely will give your message a fun, lighthearted, carefree touch. I see no reason why you shouldn’t use “nite” if that’s precisely the tone you want to convey.