I went through the interview process as a student about 9 years ago, and have interviewed many students since then from the other side of the table. Law firm interviews are generally more like conversations than grilling sessions. You are not likely to be asked substantive legal questions and you probably are not going to get any wacky hypothetical questions.
The best advice I can give is to think about your personal story. I know that sounds kind of hokey, but I promise it will be helpful. So before the interviews think about questions like Why did you go to law school? How did end up at the school you chose? What kind of student are you? Are you someone that just gets it, or do you have to work harder than others to keep up? Is there something that you’ve had to overcome to get where you are? Why did you choose the classes you chose? What motivates you to get up and go to class? What is important to you? Challenging, interesting work? A healthy work / life balance? Be honest with yourself. Think about real examples in your life that will help to explain your answers. You may or may not get these specific questions, but if you know your story, you will be able to work in bits and pieces no matter what the questions are. In my opinion, interviews are really about getting to know who you are, not how smart you are (that’s what your resume is for).
Be ready for the question: “So what can we tell you about the firm?” I can almost guarantee it will be asked, and, in my opinion, if the interviewer is not very good they will ask this question about 5 minutes into the interview. Be prepared with at least 5 or so questions in response just in case. I personally would avoid asking questions about the current state of the economy in the on-campus interview (I do think you want to get a sense of the firm’s financial health, but I’d try to do that with research online or get at those questions in a callback interview). Try to focus on the positive. Look on the firm’s website to see if there are any things that the firm appears to be particularly proud of – a big commitment to pro bono, an extensive training course for new associates – and ask about those things. Do a quick check of the bios of your interviewers to see if you have any common interests or connections. And you can always ask questions about the summer program: What will I be doing, Will I have a mentor, etc.
Be ready to say why you are interested in the city that the firm is in, particularly if your resume doesn’t show a connection to that city. But be honest. If you don't know much about the city, ask them if they could tell you why they were drawn to work there.
Know your resume. You will be surprised how many times you’ll get the question, “so I see you did so and so, tell me a little bit about that.” Have some quick story or anecdote for every item on your resume that shows why that thing was important enough to make it on your resume.
Avoid questions like about starting salary at your firm or hours worked. While I think those are important questions, there are better ways to find these things out. In the interview they can make you seem greedy or lazy.
Hope this is helpful. Good luck!