You need pointers for photography in one of the most photogenic cities?
Well, ok, then.
The Centro Storico (historic center) is full of beautiful architecture, plazas, fountains, monuments and people. Very touristic though so have in mind that your photos will be full of tourists. The Pantheon, the Fontana di Trevi, the Plaza di Spagna, Piazza del Popolo, etc are all over there. The Colosseum is a bit further down.
Then you have the calmer but also beautiful streets of Trastevere across the river.
Of course don't forget to visit the Basilica of St.Peter and the Vatican.
If you want a park, the Villa Borghese is interesting.
There is good public transportation but you can walk around all these sites if you aren't weak on legs.