I'm not sure who I would be like in terms of an individual. I realize that each justice is unique and driven by their own political, ethical and legal mindsets. But I tend to think of the court itself as an entity, even when it is split as it often is today.
Having said that, I think I would like to be a bit like Sandra Day O'Connor (if not built similarly). It seems to me that Justice O'Connor was more concerned about the law than the political landscape. Even when I disagreed with her opinions, I respected her reasoning.
My view of the law is based on the ideal that we are in a common-law rather than a civil law society, and that is a good thing. I would want to view each decision from a fresh-start perspective, rather than a preconceived notion of "what-I-think-is-right." As a judge, I would view it as my role to determine what the law said - not what ought to be. That law includes first the Constitution, second the intent of the legislature, and third the interpretation of the courts. I would not take lightly the idea of dismissing jurisprudence which has endured the the test of time, especially precedents built on precedents. I would, when absolutely justified by the situation, vote to correct what I thought was improper interpretation of law or inappropriate application of precedent, but only to the extent necessary to bring the law back to its proper place. I would take even more care when making judgements concerning the Constitutionality of legislation. I would never vote to overturn a law with which I disagreed unless it clearly and directly violated the supreme law of the land. At the same time, I would vote without hesitation to overturn laws that did violate that law.
To the extent possible for any person, I would never allow my personal religious beliefs or political views to supersede well-established precedent or the clear and Constitutionally sound intent of a legislature. I might as well vote for or against laws about abortion, homosexual marriage, and other such sensitive topics depending on what arguments were used, what specific legal issues were raised and what was more in line with the Constitution and precedent.
In other words, I would try to be objective and interpret the law according to the law, and the will of the people and their elected representatives. How successful I would be is anybody's guess.