Near the main train station: Alessio (really good food), Via del Viminale 2/g. It's on the corner, and it's downstairs. Gelato: Verde Pistacchio, has a vintage Vespa out front, and the counter is a converted VW Bus, Via Nazionale N 239.
Best coffee (from the train station, it's closer to the Spanish Steps): Sant 'Eustachio Il Caffe, Piazza S Eustachio n.82.