I agree about approaching the court officers. You might want to print out what's required for the assignment, as well as course details, including professors contact info. I suspect that they might direct you to the most interesting cases.
It is public. Some cases are closed but that is uncommon. Supreme court might be more interesting than civil. I would go to court and ask a court officer what you can observe. As long as you are nice, imagine they will point you in the right direction.
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