There is an abundance of short-term opportunities to go overseas – some good and some bad. It is recommended that you read When Helping Hurts before going on a short term trip and consider whether the trip you are planning on going on is focused on long-term sustainable principles described in this book.
Once you've done that, check out the following places to go on a short-term trip:
A clearinghouse for short term missions with around 2,000 opportunities!
The Edge is a 6 to 10 week summer mission trip for young adults in which you will work alongside field workers, learn a new language and culture, and grow in your understanding of God, yourself and His call on your life.