Most clerical students in Rome live in a collegio. This collegio was established for Russians and others by Pope Pius XI in the 1920s. It's across the street from St. Mary Major, near to Roma Termini.
Ring the bell and the porter will bring you into the gift shop on the main level. Also, after the sung Liturgy on Sundays in their attached parish, they often have tea time in the grand salon of the college which is nice to see, too.