Not only did they have street food, but it was where most urban residents got their meals! This is a copy from a previous post I made:

Roman citizens (especially in Rome itself) usually lived in insulae, basically small apartment buildings, and only the wealthy had an individual house (a domus) with a kitchen and staff to cook. Apartment-dwellers would often have a charcoal brazier, but it was dangerous to use inside. More commonly they would purchase food from a variety of street stands and restaurants.

A popina was an establishment (usually open 24/7 or close to it) that sold simple foods like porridge, sausages, fish wrapped in parchment, and chickpeas. They also provided an easy place for illegal gambling or for prostitutes to meet clients. Popinae were the usual meeting places of the lower classes outside of the home, including off-duty slaves, which gave them a poor reputation. Tabernae and thermopolia sold all of the above as well as prepared dishes like stews, meatballs, and roasts. Tabernae were frequented by all levels of society, as they were often located near business and entertainment centers and provided an easy place to stop for lunch and socializing.

The primary drink for all classes was wine in some form, as it was produced all across the empire. Winemaking was a mature industry during the days of the Empire, with wines from different regions having their own reputations, styles, and ever-changing popularity just like today. White, red, and rose wines were all common; rose may have been the most common, as it's the simplest to make (dark and rich reds require you to engage in extra maceration and a longer production period to fully infuse the compounds from the grape skins, while whites require you to skin the grapes first). Falernian wine is the most famous of Roman wines, though its popularity changed with time; Falernian aged as long as 200 years was drank, though Pliny admitted that it was so thick and highly concentrated that it was almost undrinkable. And also like in real life, counterfeit Falernian was rampant!

Wine was commonly adulterated for flavoring and preservation. On the positive side, you had honey wine (mulsum) and spiced wine (conditum). On the negative side, you could find seawater, chalk, marble, and pitch.

Wine was typically watered down at a 3:1 ratio of water to wine before drinking, as it was intended for hydration when you weren't partying or relaxing. Wine in drinking establishments was priced by the sextarius (a unit of measurement equal to about 1.15 pints), presumably already watered down. A sextarius of watered-down wine would have an alcohol content equivalent to about one modern glass of wine, enough to get a very slight buzz while keeping you hydrated. Drinking undiluted wine when you weren't in the appropriate setting was considered barbaric and public drunkenness was embarrassing.

As Romans bought so much of their food, you might be wondering how much they paid. The usual money that citizens would deal with was the silver denarius, which was divided into 16 bronze or copper asses. A typical wage in Pompeii in 79 AD was 1 denarius per day. Surviving records from Pompeii (such as menus written on the walls of tabernae and popinae) indicate prices of 1 to 5 asses for wine depending on quality, 1 as for a Roman pound of bread (about 0.73 American pounds), 2 asses for a sausage, and 4 asses for a meat cutlet. It would be perfectly possible for all but the poorest Romans in a city to survive on purchased food.