I like nitch, but it makes sense that a lot of people say it the other way. Every foreign language I've ever studied pronounces the "I" sound like "ee", whereas in English we generally pronounce it either long or short, as in "vibrator" or "MILF", and the "ee" sound usually is usually spelled using "ee". I can see why someone whose native language isn't English would naturally gravitate toward the "ee" sound.
Also, if you consider the fact that the word comes from French and retains kind of a French spelling...and it's very easy to make a case for the "neesh" pronunciation. We say things like "quesadilla" or "tortilla" the Spanish way, even though that's not the way "ill" typically sounds in English.
I still like nitch, though.