The cheapest accommodation in Naples is in the area around the Central Station (from 30–35 EUR). Of course, on the outskirts you can find even cheaper hotels, but tourists are not advised to stay far from the city center. In addition, you can stay in hostels, where a bed costs at least 25 EUR.
By the way, keep in mind that in Naples, a city tax of 1–4 EUR per person per night is added to the room rate.