Ok, I know I'm taking the easy road here but according to Wikipedia, Neapolitan, like other Romance languages, has partly evolved from vulgar Latin but also has a pre-Latin Oscan influence. An example is the pronunciation of the group of consonants "nd" (of Latin) as "nn" (e.g.- "munno" (world, compare to Italian "mondo"). In addition, Neapolitan also seems to have been affected by Greek. Unfortunately, no examples are provided in Wikipedia.
Interestingly, Griko (or Grico) is a modern Greek dialect which is still spoken in the region in Southern Italy which roughly corresponds to the ancient Magna Graecia. So I think it is fair to say that Greek has had a strong influence on most dialects spoken in this part of Italy even if most are nowadays predominatly Romance languages. Probably, as with all major Romance languages today, the most obvious traces of Greek are to be found in their lexicon (as docoflove already suggested).
There are other interesting websites (some of them only in Italian) which touch on the subject:
Vierb Vulant
OmniglotNapulitano
Napoletanita