Moderately Priced Lodging in Cinque Terre, & Rome

You'll first have to provide some clarification on your criteria for "moderately priced". It would also help to have some idea which of the five Cinque Terre towns you might like to stay in, or which part of Rome you might prefer.

Without more specific information, it's difficult to answer your questions.

You might start with a booking engine like Booking.com to get an idea of what is available. Especially in Rome, it is a more efficient way to search. Then you can decide what "moderately priced" means.