I wouldn't plan to arrive much before 10AM at the check-in counter. Last time I got there at 9AM I found that 1K/Business/First class lines were not open until 10AM and there were signs directing you to the domestic terminal. Save yourself the time and just arrive at 10 - unless you'd like to visit the museum which I highly recommend, or to visit any of the pre-security shopping, all of which is quite pleasant.

Echo all the comments about Carol and the great Bloody Marys!