Hmmm. Well, I'd be inclined to advise you to get AWAY from the touristy areas, especially those that are tour-group magnets, like the Spanish Steps. One of the best meals we've had in Rome was off the beaten path a couple blocks from the Trevi Fountain. Unfortunately, I couldn't tell you the name of it. If you want a nice sit-down meal, then there are a number of nice places on Via Veneto (top of the Spanish Steps + a couple blocks) just outside the major hotels. While we always stay there, at the Excelsior, we tend to eat elsewhere. We always eat at least once at a little place on the Piazza Popolo (contradicting my advice to avoid tourist areas)!!! But it's mainly for the ambiance.
Honestly, if you like Italian food, it's hard to miss. My only advice would be to ask the locals where they go with their families. You may not get the best scenery, but it will almost always be the best food. We intentionally try to get "lost" on back streets for this very reason. Only once have we been remotely disappointed - and that's after eating at least 5 or 6 dozen meals there.
One word of advice, though. When they bring a menu, it will say Primi and Secondi, as in "1st and 2nd Course". Their Primi (pasta) course is plenty, especially if you start out with caprese salad or antipasto. Unless you're a major wine snob, then take a chance and just ask for a pitcher of their house wine. It is better than 90 of the mainstream "daily" reds we drink here in the US because there are no sulphites.. and because, well, because it just tastes better in Roma!! A pitcher (4 glasses) will cost you about 6 euro at most places!! (I'm assuming that with two teenagers you're not doing haute cuisine every meal.)
FWIW, we've only had the hotel breakfast ONCE in all our trips to Italy. We much prefer to hit the streets on an empty stomach, then stop at the first cafe for a panini (sandwich) and espresso. The whole thing will cost ~ $3/person, max, and is a GREAT way to start the day.
If you have any other questions, feel free to PM me or Carlo.