I could be wrong on this one, cause there are many other common outreaches like sports, puppets or drama, but probably the easiest outreach to start around the world right now is an English as a Second Language Outreach. It is amazing to see how many opportunities for classes are available in so many places (besides Australia, South Africa and other countries that already speak English).
People here in Porto Alegre value English lessons greatly. When I walk to our church, about a mile away, I pass three English schools. They are all over and it is a great privilege to have an American as a Professor. I have never really wanted to teach English, but I think that I am going to start more classes now because of the great opportunity to make contacts. I currently teach one student, Juarez, because another missionary here is on furlough in the states and asked me to teach him. It started off rough, cause I didn't know too much about what I was doing, but now it is not too bad. It is neat to build the relationship and see progress in his English.
What about where you are at? Be it in the states or abroad. Are there those opportunities? Someone recently told me that they thought that Christians were missing the boat on the opportunity of helping out all the Hispanic immigrants that go to the US. ESL would be a great outreach for them!