There are times when out of town girls come to New York and set up a few dates through Shadchanim.
In general, I think that a guy should go to the girl. I would not allow my daughter to go to the guy. If he doesn’t value or respect her enough to come to her the first time, he will never respect her after they get married.
When a guy is ready to get married, he should be able to tear himself away from Yeshiva long enough to meet a girl. After all, getting married is also a Mitzvah, isn’t it? Or because of Bitul Torah, should they have the date in the Bais Hamidrash?