“Buona domenica.” It’s what you say here instead of “have a nice weekend”. The reason for this is because, generally speaking, stores are open Saturday, businesses and schools too. So people don’t get the whole weekend off, hence “buona domenica!”
Oh sure, some of the big box stores are open on Sunday just like in the US. But the smaller places like banks, businesses, family owned places close on Sunday. It is a day for families to get together for a big lunch. Either at home or in a restaurant.
Speaking of restaurants, since they are usually open on Sunday for the big Pranzo, they choose another day of the week to be closed. Monday is a popular closed day but it could be any day of the week. They do this throughout Europe. In Germany it is called ruhetag or day of rest. There is no equivalent word in Italian. It usually catches Americans by surprise so be sure to check that your restaurant of choice is open the day you want to go!