Nebet Tepe is the northern end of the Old Town and the reason there is a city here at all. It is a rocky outcrop with the ruins of successive fortifications on top — Thracian foundations, then Greek, Roman and Byzantine walls built on the same line, plus the remains of cisterns and a secret passage down to the river. The ruins are unfenced and you walk over them.
Come for the view, which is the best free one in Plovdiv: the Maritsa river to the north, the Rhodope foothills to the south, the tiled roofs of the Old Town immediately below, and Bunardzhik hill with the Alyosha Monument on the skyline. It is the standard sunset spot, so at that hour it is full of students with beer from the kiosk at the bottom.
It is a stiff ten-minute walk up cobbles from Hisar Kapia, and there is nothing at the top but the ruins and the view. No entrance fee, no gate, open whenever.