The cheapest accommodation in Naples is near the Central Station (from 25-30 EUR). Of course, on the outskirts you can find even cheaper hotels, but tourists are not recommended to climb far from the center. In addition, you can stay in hostels, where a bed will cost at least 17 EUR.
By the way, please note that in Naples, a city tax is added to the amount of room payment - 1-4 EUR per person per night.