We spent 12 days in Rome and Florence during the week of Easter and we ate out every night. We are a family of four with two teenagers (boys). Although we treated ourselves to a couple of expensive meals (over 200 Euros per dinner) during our stay, we spent most nights dining at more reasonable priced restaurants.
There is no need to order an antipasto, a primi and a secundi at most restaurants. I have been to restaurants which you can order a couple of appetizers and 4 pasta dishes (or 4 secundis). We were at a restaurant near the Pantheon and there was a family that only ordered 4 pizzas (each pizza cost 9Euros) and half carafe of wine and water. At another upscale restaurant in Florence, we sat next to a young couple whom only ordered 2 pasta dishes (about $9 Euro each), a dessert and some wine.
Most of our bills were in the range of 80 Euros (for 4 persons) and sometimes 110 Euros if we order steak (you have to order a kilo for two persons at most restaurants in Florence). On our last night, we were at a restaurant right at Via Del Corso (Florence), which is the center of tourism and our bill was 66 Euros (2 appetizers, 4 pasta dishes, wine, water and a tiramisu).
There is no need to worry about the food quality in Rome or Florence. Unless you are really unlucky, your pasta dishes will taste better than the ones you will eat in high-end restaurants in New York or any US major cities. The reason is that everything is freshly made, the cream, butter, egg, bacon taste differently than here. Therefore, it does not make sense to go to the most expensive restaurant when you know you will have a great meal everywhere.
I have read a few postings on Chowhound that say that it is not proper to order little and that restaurants will not make money of travelers like us. My response to it is that, even during one of the busiest week of the year, which is Easter, they are still so many restaurants in Rome and Florence that barely fill up every night. At busy places such as Pantheon and Campo De Fiori, each restaurant had host trying to invite customers into their premises.