About 50 km (31 miles) east of Naples, still in the region of Campania, is Partenio National Park. The park consists mostly of woodland spread across low-lying mountains and ravines, with plenty of open space and picturesque views for hikers, as well a few very nice waterfalls (Cascatelle and Acquapendente) and some quality caves for the spelunker in you (particularly on the mountain slopes near the Camorra-run town of Nola. The Camorra, for the curious, is a legitimate mafia organization).
Another off-the-beaten-track sight that is definitely worth your time is the Guglia Rocciosa in the town of Pietrastornina, a limestone spire that looms above the town. Visitors can make reservations to climb this unique outcropping to get a view of the national park and what remains of the military installation at the top.
The ocean isn't the only thing worth seeing if you're visiting Napoli; head out to Partenio National Park for a more diverse offering.