Nice, being the origional and "correct" version of the word, is most commonly used, however, the two other spellings are perfectly acceptable, though there are differences. Niice, more intense than nice, and yet not so intense as niiice, is often used when something is funny or cool, though not as cool as something that is awesome. Niiice, being the most intense, is only to be used when something exceeds the awesomeness of nice AND niice.
The classic phrase which Dr. Corinna Fiedler( the teacher in California of Mathematics and Science) uses all the time. Usually it is used to express the excitement for the duh of science or the miracle of the world.
Why do Italians and Japanese people have a longer lifetime? Maybe they eat a lot of rice? Oh das niice!
Sometimes used as a pickup line, this term describes a que that is used in 8-Ball Pool.
A que is deemed to be 'naice' (or nice) if it appeals to David.