We've stopped going to a park on that first day. We usually wind up with a flight that requires us to wake up at @#$ o'clock in the morning. By the time we've flown, limoed, shopped and unpacked, we're pooped. If we go to a park we just get crabby.
Our last trip we arrived with a Cape May dinner PS in our pocket. So we just strolled comfortably around the Boardwalk, played some arcade games (my son won a stuffed pug, of all things, and had to go back another day to win it a "mate"), peeked at this year's merchandise in the stores, and bought baked goods for the next day's breakfast. After that we sprawled for an hour or so at SAB, lounged through the buffet, and turned in for the night.
We really enjoyed the low-pressure entry to our vacation, and the next morning we were right there at EE for the MK.