What businesses/organizations do you all feel need help expanding their advertisements through social media?
I would consider an agency...if you didn't know, there are companies out there that help business focus on their social media strategy and plans. A lot of general marketing agencies do this as well. Look at Likeable Media in NYC, if that's convenient for you. And I know they offer internships. If you get to work in an agency, you'll likely get exposure to different types of business that have different needs and requirements and this experience will help you hone your focus on where you might like to work in the future. Good luck!
If you're looking to learn, find the people doing social media right. Then you can apply the skills to any business or organization. A good start would digital/social media advertising agencies. Do you follow Gary Vaynerchuk or Vaynermedia? Great reading and resource.
There are several for profit and non profit organizations that are always looking for social media advertising and talents.
Question: Why do you want to do social media? If you are good with advertising in social media. I would recommend start advertising your skill sets through various social media channels. First one being this one.
Hope that helps!
Assuming you are still a student or just starting your career, consider approaching this a little differently. Instead of looking for who needs help, look for who does it best. They are the ones you want to be alligned with now either though an entry level position or internship. Searching online or within industry publications will help you identify those who are considered the most innovative in this space. Good luck.