Do you mean the opening stage which starts and ends in Napoli on 4 May (156km road stage), or the TTT the following day on the nearby island of Ischia?
The official Giro website has the best maps of the stages I have seen - click on the tab "list of the stages" for links to each stage:
If you're only in Italy until 5 May, you probably won't be able to make the TTT unless you have a late flight out of Napoli (or very late flight out of Rome: Napoli - Rome Ciampino airport is about 3 hours drive, probably 3.5 hours to Fiumicino airport). I'm guessing the team buses and organiser's vehicles will fill a ferry or two off the island after the stage finish. From memory, the ferry ride from Ischia takes over an hour, then it's half an hour or so drive to the airport assuming town isn't gridlocked (as it can be near the port). If driving, trust a paper map over your satnav - at least in 2008 both TOMTOM and ROUTE66 had dodgy data including roads that went over cliff edges and along (literal) goat tracks. On the other hand, if you can extend your trip Ischia is very pretty; stay at a hotel on the South side of the island with thermal baths and a private beach at the bottom of the cliff.
You could probably catch some of the pre-departure fun of the opening stage which looks like it's leaving from the main square in Napoli, then hang out for a few hours doing touristy things (eat some pizza Napolitana) before catching a bus to the stage finish.
Driving in Napoli is not for the faint-hearted, and unless you're totally nuts you DON'T want to ride a bike in the city. In terms of craziness of the traffic it ranks up there with anywhere I've been, which includes Bangkok, New Delhi and Saigon. Picture a road with three marked lanes, but 6 cars driving on it side by side. Then picture 5 of these roads leading into a roundabout. You also need to be prepared to pay a gratuity to someone to watch your car for you while it's parked, to make sure it doesn't get damaged or stolen. And there are some streets that it's not possible to drive into without ignoring "One Way" or "No Entry" signs, even though you can see cars in there. And don't expect your satnav to be correct in town either! On the positive side, there was lots of beeping and waving arms out the window, but I didn't encounter any road rage.