Kosher restaurants in the Ghetto will be closed April 6 PM (Shabbat), April 7, and April 8 (yom tav). April 8 is Easter Sunday. Easter Monday is still passover but I can't remember if kosher restaurants are open then. Other restaurants outside the Ghetto will be open. I'm copying and pasting from a blog post I wrote last year. There shouldn't be much variation in 2012:
"While most Rome dwellers will be dining at home or in their hometowns somewhere else in Italy, visitors will have to compete for tables at the restaurants that remain open. Here is a brief round-up of places I recommend for Easter Sunday and Easter Monday (or any other time, really):
Antico Arco: creative cuisine which draws inspiration from the ingredients and recipes of southern Italy. Expensive, but not excessively so. Open for dinner only both Easter Sunday and Easter Monday. Call +39065815274 for reservations.
Cul de Sac: This long established wine bar near Piazza Navona has more than 1,500 (mostly Italian) labels and a nice selection of cheeses, pates, and salamis. It has outdoor seating, a huge improvement on the uncomfortable benches inside. Open both Easter Sunday and Easter Monday for lunch and dinner. Call +39066 8801094 for bookings (I think they only take reservations for 1230pm and 630pm).
Da Danilo: Roman food with a hint of modernity. Da Danilo is home to one of my favorite carbonaras in the city. Be sure to specify a table upstairs. Open on Easter Sunday at lunch. Call +390677200111 for bookings.
Flavio al Velavevodetto: moderately priced Roman cuisine with outdoor seating. Open both Easter Sunday and Easter Monday for lunch. Call +39065744194 for bookings.
La Campana: Classic Roman cuisine in a familial setting. Open Easter Sunday at lunch and dinner. Call +39066875273 to book.
L’Asino d’Oro: Chef Lucio Sforza serves “Umbrian soul food” at moderate prices in Monti. Outdoor seating available. Open Easter Sunday for both lunch and dinner and Easter Monday at lunch only. Call +390648913832 for reservations."
Antico Arco, which is now open for lunch, may also be open for lunch Easter Sunday & Monday (it was last year). La Campana has gotten some bad reviews of late.