Why are the worst suburbs across state lines?

[ag]

With the exception of Gary

Actually, Newark is far more of an exception than Gary. (Now... if the OP had referred to Jersey City...)

Newark is far easier to get to from Midtown or the Village than most of NYC. PATH takes about 20 or 25 min from Christopher St. - actually, there are places in Manhattan where the subway takes longer. The bits of swamp in between notwithstanding, this would not have been a different city, if not for the state line.

[ag]

State lines cut up urban areas, making technical "suburbs" of what would have been inner city districts otherwise.

Newark, of course is (or, at least, used to be) quite a separate urban core - but then so was Brooklyn. In any case, whether it is a separate inner city, or an extension of NYC, Newark is not a suburb in any sense of the word. The same, I guess, is frequently true in other places as well.