You may already be a bit late for summer internships in some industries. I did my internship with Goldman Sachs in London (IT). I'm sure that applications for that had to be before Christmas in the previous year. I am interviewing a potential internal where I work now (Citigroup) on Monday, again an IT position. All applications had to be in some months ago.
In my opinion unpaid internships are a pretty rough deal. When I did mine I was being paid quite a bit but the costs of short term accommodation, food and socialising wiped it all out and more.