We have 2 CDCs that go through spurts of hiring / not hiring. There are many ways to look for NAF jobs when you arrive. Our weekly (FRI) base newspaper has all the listings, and you can go to the local Fleet and Family Support Office as well for assistance. In the meantime, you may want to look through the NSA Naples website (www.cnic.navy.mil/naples) and see what you can find posted there.
If you are used to working in the NAF world, you shouldn't have too many problems finding a job (although you may need to wait for one to open up in childcare). There are divisions for NAF opportunities - those for US and those for our Italian local nationals, but the listings are very clear on which is which. If you are interested in APF (GS billets) there are occasionally those as well.
Believe it or not, spousal preference actually means A LOT here (unlike the US) and generally trumps everything (provided the person is qualified) except for spousal hires with veteran preference. Just one warning - be sure to apply for only those jobs you are actually interested in as you can only use spousal preference once, and if you are ever offered a job and turn it down, you will lose it.
Hope this helps.