Papa Rex means Pope King, the last of which was Blessed Pius IX.
The Ristornate Papa Rex is a really fun place to eat, and its just next to the Vatican (Via Aurelia, 87).
It's a big place open for lunch and dinner and each evening they have a dinner show with live music including opera arias and traditonal Italian folk music.
They even organize theme dinners upon request - perfect if you have a group of high school or college kids.
See here: http://www.paparex.it/.