In Rome there are many place located on hills where you can admire Rome by night:

– Passeggiata del Gianicolo on the Janiculum Hill (just cross the piazza until you arrive to the wall facing the whole Rome): here’s the place on Google map and here some pics on the web;
– Passeggiata del Pincio on the Pincian Hill (then keep walking Viale della Trinità dei Monti, you’ll pass in front of Villa Medici until you’ll arrive at Trinità dei Monti, you can get other awesome glimpse of the Eternal City along the way!): here’s the place on Google map and here some pics;
– The so-called “Vialetto degli Innamorati” (the walkway of lovers) at the Zodiaco belvedere on Monte Mario Hill (you can reach it only on foot or with your own vehicle and you don’t have to dine at the restaurant to have a walk along the belvedere): here’s the place on Google map and here some pics.

Plus three secret places:
– Via Piccolomini: map and pic;
– Viale Aurelio Saffi at old Monteverde: map and pic;
– Via Sacra in the Roman Forum: starting from the Colosseum, take the Via Sacra and walk along the path you’ll find open: you’ll get an awesome view of the historic center of Rome by night! Map and pic.

Hope this helps!
MR