If you must actually see the Trevi Fountain, wake up at 6am and walk to it. It’s about the only time you’ll see it in daylight without the crowds.
And when you’re done, go get your morning cappuccino and croissant.
7am, and the crowds are just arriving at the Fontana della Barcaccia (“Fountain of the Worthless Boat” ) by the Spanish Steps.
Sketch that fountain and then it’s time for another coffee. If you’re at Cafe Gilli, they can fancy it up for you with something from the bar.
By sunset, the Fountain of Neptune has it’s share of the crowds, but I join them and sketch a corner of it anyways. It’s hard for even a marble statue to look grand and dignified when there’s a seagull sitting on it’s head.
There’s drinking fountains all over the city and the water is cold, so fill up your water bottles when you pass one.
Last bits of advice, really . Look up. A lot. Besides the domes, the rooftops and chimneys are fascinating. Even just really ordinary ones.