Rome is not a cheap city, but it is much cheaper than many other European cities and there are plenty of reasonably priced and low-cost alternatives for students.
Food is great and generally inexpensive, especially if you shop at a supermarket or local market stalls. Eating out, movies and other leisure activities are, again, less expensive than many other European capitals. A meal at a restaurant will vary depending on where and what you wish to have, but a pizza and a beer in a pizzeria costs about €10-12.
Public transportation in the city is also relatively cheap - €1.50 per journey - and much cheaper if you invest in a monthly or yearly pass. Trains are also far cheaper than in other European cities.
Moreover, you can take advantage of a large range of student offers and discounts available at clubs, museums, sporting events, etc.
Your greatest expense will be housing, depending on which area of Rome you choose. (Please note: the cost of renting an apartment described in the link below refers to the cost of the entire apartment, whereas 3-4 or more students usually share an apartment.)
On average, you will need at least €800-900/month to live in Rome. Although you only need proof of about €500/month to apply for your student VISA, please be warned that this is not enough to live in Rome.
For further information: up-to-date information on costs of food, housing and leisure activities in Rome.
(Photo: Flickr, Giasco)