I've been to several times lately Rome and I must say that I have found Vyta the best place a Rome Termini and surroundings where to have breakfast, lunch or an aperitif. What is Vyta ?. Vyta is a chain that in addition to Rome is also located in Milan, Turin and other Italian cities. I don't know where it is in the other Italian locations, but in Rome it is in Central Station of Termini.
Why is it the best and most suitable place for travelers? First of all because it is located in the station, a place of excellence for travel, arrivals and departures. If you are early, if your train is late you can always take refuge from Vyta, which, for us travelers (and not only) has a open wifi network :O
A great news that of the wifi in a station where everything is paid, starting from the downstairs bathrooms. In short, I recommend Vyta for the connection and the location, but also for the food. All very accurate, from the presentation of the food to the clothing of those who work there. It doesn't even feel like you're in an ei station prices are really handy. I recommend it.