Palace of Caserta

The Palace of Caserta was one of the largest Royal residences built in the XVIII century, comparable only to Versailles, though the two residencies are different for architecture and style.
The Palce of Caserta is a Unesco World Heritage site.
There is also a 12O Hectares park with majestic fountains and hidden places.

It's possible to get there by train from Naples

http://en.wikipedia.org/wiki/Palace_of_Caserta

Pompei and Ercolano

Pompei and Ercolano are two of the most famous Italian touristic sights. As you might know, the cities were destroyed and buried by ash by the Vesuvio eruption during the Roman Empire and stayed untouched until they were discovered and restored in the XVIII century. These ruins, as big as a city, offer a great overview over roman life, with wonderful mosaics.

It seems it's possible to visit them by train with the Circumvesuviana, a suburban train with few lines going up or around the volcano Vesuvio.
Pompei is half-way to Sorrento. By train, from Naples to the coast of Sorrento is just one hour! In the sunny days the view on the Gulf of Naples and Vesuvio is amazing!

Historic center

Naples' historic center is Unesco's World Heritage, and it's considered the largest in Europe. It's a mixture of styles: medieval, renaissance and baroque. The best way to visit it is just strolling aimlessly, in order to enjoy the alive and exciting center full of people shouting and speaking like Enzo! You'll see that Naples can be frenetic and slow at the same time.

Some parts of the old center are considered dangerous especially at night, above all Quartieri spagnoli, but during the day two poor travellers like us shouldn't have any problem....

http://en.wikipedia.org/wiki/Quartieri_Spagnoli

Spaccanapoli

Spaccanapoli is the most central street of Naples, the one is cutting the city in the middle. It's considered the best place to experience the real lifestyle in the city: food smell from the windows, black market in the street, little corner shop selling amazing things, people shouting and motorini speeding up: Naples!

Gulf of Orosei

I have to be honest, I don't really know this part of the island, but I've always heard amazing things about it.
The gulf of Orosei is located in central-eastern part of Sardinia. In the northern part of the gulf  there're sandy beaches and pine trees forests, the southern part is more typical for its big cliffs.
For the richness of animal species and vegetation, the Gulf of Orosei has been declared National Park.
A friend of mine recommended me to go in a sustainable camping that should be open also in November. They offer bungalows for 4 or 6 persons for reasonable prices (also because we're in the low season).
The camp is located in the valley of a river, but at the same time there're tropical beaches and other places to explore in the near surroundings, so we shouldn't spend lot of time on a car.
Give a look to this video:

http://www.portososalinos.it/

Green Coast

The Green Coast, or Costa Verde, is considered one of the most amazing places of the island. Until the first half of the XX century was an important mining center (also my grandad used to work there), but once this activity wasn't that profitable anymore, mines closed, people left and nature flourished.
Green coast takes its name from the impressive vegetation, and to get there you first have to pass some mountains. On the way to Costa Verde you'll find many abandoned mining ghost towns, by this time desert, that makes the enviroment more similar to a western movie. But once you start going downhill, the view on the sea is breath-taking.
Costa Verde is perfect if you want to stay in the nature and enjoy of the silence. Imagine than in this part of Sardinia, exactly in Piscinas, you can find the biggest dune sand of Europe.
As the local economy based on mining failed, people start to develop a low-scale form of sustainable tourism, far from the fancy-posh-disneyworld style of the tourist resorts in the north-eastern part of Sardinia.
Small guesthouses and bed and breakfast run by locals, offering local products, make the stay in this part even more unique.

I guess it's even possible to rent a small flat in some super tiny places near the sea.

Stintino

Stintino is a popular tourist resort 35 Km from Sassari, in the north-western part of the island.
Quite crowded in the summer, in autumn is probably half-desert.
White sand and amazingly transparent-turquoise water makes this spot worth of a visit.