Law Internships

As a high school student, obviously law internships are hard to come by, as many law firms want law school students. There are some firms that accept high school students, but many had very early deadlines. I was looking into possiblty finding a smaller law firm in new york city, because they may not be as busy and have less people looking for internships. Would it be a good idea to go to the city one day and ask around at law firms if they are looking for any interns this summer? Thanks.