An important meal to most Americans, less so for southern Europeans and Italians. A carafe of coffee (or tea or chocolate), usually with milk (caffee latte), and a roll (usually a brioche, though croissants are common in pricier hotels). No juice, eggs, or bacon. In upscale hotels juice, eggs and bacon are available, at a price.
Picnics:
These are useful, as well as enjoyable in good weather, to reduce meal costs or extend your day at places without food service like the Forum/Palatine or Ostia Antica. And don't be afraid at other times to picnic on your bed in your room ... it's a dandy, occasional idea if you're running tight on your budget.
You'll find some general groceries (alimentari, or, literally 'foods, or food stores) at which you can purchase some or all of your needs. Alimentari carry a range of goods (including laundry soap, for example) but are usually small.
Often, though, you'll need to visit several shops: the salumeria (sausage shop), frutteria (fruit shop), cheese shop, bakery, and so forth. One or more of these will usually sell bottled water and other beverages as well. Part of the joy of an Italian picnic is assembling the ingredients. And in most cases you'll be overwhelmed by the variety of choices, and the quality. Americans are accustomed to one type of salami, perhaps two, prepackaged. If you're indecisive you'll never get out of the salumeria given the choices of 'salami' you'll find.
Since Italian cooking is based on fresh food, the custom for cooks is two trips to the store for lunch and dinner. You'll find, therefor, varied opening hours. Alimentari often are open only late in the morning and late in the afternoon. Some specialty stores are open all day, as are the occasional equivalent of a delicatessen where you can buy most everything except perhaps the fruit.
Your hotel personnel will be able to tell you where the nearest stores are. You'll rarely have to go more than 2-3 blocks. Do check on the hours though ... picnics usually require purchase the preceding afternoon if you'll be leaving before mid-morning.
'Un etto' (a hectogram - 100 grams) will get you almost 4 ounces of meat or cheese. 'Un quarto' gets you more than twice as much (250 grams), enough for two sandwiches. If you're unsure of quantities you may find a peek at European Weights and Measures of interest.
Picnics (whether for the park or for back in the room) often take a few stops to put together. The effort is repaid by the quality, and the opportunity to do as the Romans do.
Dining
About Restaurants:
Restaurants are open from Noon to 2:30p.m., roughly. Some open as late as 1:00. You can't eat a restaurant lunch either early or late. Restaurants reopen for dinner at perhaps 7:30p.m. - you may find some opening at 7p.m., and many not until 8p.m. or 8:30p.m.. Bars and sandwich shops are open most of the day.

