AS a young student in Singapore, Sharon Lai decided she'd like to attend college in the United States. Although she didn't have a specific school in mind, she had an idea of where to look."I had heard that Boston was a university town," Sharon says, explaining that she focused her search on schools in the area. Today, she's a sophomore at Boston University (BU). Sulochana Vivekananthan, a BU senior from Sri Lanka, attended Wesley College in Dover, Del., for her freshman year. After nine months of relative isolation, she decided she'd rather attend a school in Boston, where several of her friends from Sri Lanka were already studying at Harvard and Northeastern universities. Like Sharon, Sulochana chose Boston first and then began looking for the college that best fit her needs. "I wanted Boston and I wanted a university that has a large international student community," she says. The difference between Dover and Boston was clear immediately. "In Boston, I can go anywhere I want. The city has so much to offer. I just have to hop on a T [subway trolley] or a bus. I can go for a movie if I want. I can go to see museums. I can go for a concert. It's just up to me what I want and have time to do." International students have long been attracted to Boston's cosmopolitan flair and easy accessibility. But the enrollment of international students at area universities is increasing. In some cases, college officials are aggressively recruiting students from overseas. Currently, at least 20,000 foreign students attend colleges and universities in Massachusetts, according to Clare M. Cotton, president of the Association of Independent Colleges and Universities in Massachusetts. "One of the main reasons for the interest in the international market is to make up for the students who have not bothered to be born," Mr. Cotton says. The entire US is in the midst of a demographic downturn in the college-age population. But the Northeast has been hardest hit; the college-age population in Massachusetts dropped nearly 30 percent between 1984 and 1989, Mr. Cotton says. The situation is "putting renewed pressure on all these institutions to define more clearly their niche and figure out how they can attract adequate numbers of students," says Richard M. Freeland, dean of the College of Arts and Sciences at the University of Massachusetts, Boston. In order to keep admission standards high, some colleges are forced to look overseas for students. Although the region has generally attracted the majority of its international students from Western Europe, the Asian student population is increasing, says John C. Hoy, president of the New England Board of Higher Education. Ten percent of Boston University's entering class this fall is from overseas, and the largest representation comes from Asia, according to the university. Historically, Dean Freeland points out, the competition for students has driven the progress and increased prestige of Boston colleges. "As the competition intensifies locally," he says, "these institutions reach out first nationally and then internationally to try to find new constituencies." "This is without question a growth area," Mr. Hoy says of international student enrollment at the range of Boston colleges. Nevertheless, the economic recession coupled with the shortage of college-age Americans present daunting challenges for the region's schools of higher education. "For the next five years - at least," warns Cotton, "it's going to be very tough to be a college in Massachusetts, state or private."