At one time, and probably even now, in many countries there are student exchange programs. I think more of these programs, extending it to even general cityzens, should be organized by NGOs and non-profitable or government sponsored cultural activities.
The different travel and tourism schemes should have interesting offers to far away places like- for people of USA to Malaysia and India. Malaysia is a predominantly muslim country, and a visit to it may help many Americans realize that muslims can be kind and docile too.
Governments should insist on inviting more of honored members of society to attend diplomatic meetings - where they can go around the country, and meet the people on the streets, to understand their life and culture better and carry the knowledge back to their own country to share.