Hi Peter,
adding to Andrea's suggestions:
1) ice cream at Giolitti, between Pantheon and Parliament. It might be crowded but it is on of the best ice creams in Rome
2) coffee or whatever at Caffe Greco: it is expensive, but it is the oldest cafe in Rome, Venetian style with old paintings at walls. An aperitive for 2 will be 20 to 30 euros, but the place might be worth the money.
3) coffee or "granita di caffe con panna" at La tazza d'Oro, just in front of Pantheon. It is closed on Sundays. Definitely it is the best coffee in Rome. Granita is crushed iced coffee; panna is whipped cream.
4) A place we never tried but looks interesting: Palatium in via Frattina. It is a place where you you can taste food and wine from Lazio, the area around Rome.
Have a nice holiday!