I can always understand the use of points. There's no reason to spend money if you don't have to.

Eataly is an international chain supermarket, and is a great thing, I would not recommend you get your breakfast coffee and pastry there (typical roman breakfast) because you said you wanted a typical Roman experience.

Eataly near Piazza della Repubblica is a three story supermarket, with a pizza and pasta place on the top floor. You can always get good food at Eataly, whether to take home and cook, or to have at one of their stores, whether you are at their branch in Rome, Chicago, Japan, New York City, Istanbul, or any of the other 15 or so places where they are at, but it's not a place for a romantic breakfast. It would be like going to Whole Foods for breakfast.

The main Eataly in Rome is far away from you at Ostiense station. The one near where you are staying opened last year when they tore down one of the two McDonalds around the hotel plaza (yes, it's that type of neighborhood) and converted it into a small Eataly.

It wouldn't be bad to grab a lunch there, but it's not where you sit down and savor a coffee for breakfast, although they do have some outdoor tables on the ground floor. But there is usually construction going on, and lots of buses and noise.

Since you'll be staying near the Termini train station, another thing you can try, but definitely not for breakfast, is its new food court. It just opened last month, so I haven't been there yet. It's supposed to be something special. It has everything from a restaurant with a Michelin star chef, to many great food stalls. But again, you don't want to have your morning coffee in a supermarket or a food court.

If you just want to have your morning coffee and pastry, which is all breakfast is in Italy, just go anywhere, because otherwise you'll spend an hour trying to do this at Eataly or Termini to have a coffee known in the USA as an espresso, (in Italy it's just called a coffee) that's just 2-3 sips and go.

You could get a cappuccino which takes longer to drink, but who wants to linger over coffee in a supermarket? If you want to linger over a coffee in a beautiful plaza, that's not the neighborhood to do it. Take a cab to where you are going, and do it there.

A coffee is usually 1 euro standing at a bar. A croissant, a typical roman breakfast, is maybe 2 euro. If you get a table with waiter service you'll probably pay about twice as much for each. However, you can stay at that table as long as you want.

If you do find an interesting place when you get to the true historic center and you want to linger at an outside table for half an hour and watch the world go by, there is nothing wrong with spending an extra couple of euros to do that. Behind the counter, by law, they have to post the price of the coffee at the bar, and at a table. You can look before you decide. Depending on location, it might only cost 2-3 extra euros, but will give you a place for people watching, catching the sun, and a place to sit down and spread your map, and make your plans. It's a personal choice.

In sum, if you just need your morning coffee, go anywhere. To see historical Rome you'll have to leave your neighborhood, you just have to make a decision where to have your roman breakfast.