There's a lot from ARR's repertoire that I think Westerners would enjoy, but most recently, here are my picks to sell to a Western audience (keeping in mind songs that would not sound too foreign or exotic for Western ears, even though there are better songs).
Tu Bole Meherbaan Ishq Ada male Rehna Tu Taxi Taxi Dil Gira Dafatan Masakali Dil Ka Rishta Mastam Mastam Shano Bekha New York Nagaram Guzarish Nazrein Milana Kabhi Aditi Jaane Kyun (female) Kahin To Ru Ba Ru Khoon Chala Jaage Pray for me Brother Mohobat Hain (Taj Anthem) Yeh Jo Desh Hai Tera
