re: Paris/Barcelona/Rome trip in mid-May...I need some recommendations

Of the three, Rome probably requires the most careful attention in order to eat well. The historic center is so hugely overrun by tourists all year round that restaurant/cafe/bakery quality can be incredibly bad unless you know where to go. Fortunately, Katie Parla's Rome recs are always spot on; she actually lives in Rome, so her info isn't out of date. Here's a link to her Rome guide: LINK