Solo, Castle Hill (Colline du Château) works.
The single best free view in Nice — the whole curve of the Baie des Anges and the terracotta old-town roofs laid out below, with a pleasant shaded park and a man-made waterfall up top. The 'castle' itself is long gone (just ruins), and you'll either climb ~200 steps, take the lift, or ride the little tourist train.