On our 4/5/03 Eastern cruise, most things opened at noon for reservations. Here is the list from the Welcome Aboard flyer we received when we checked in at the port:
Palo reservations - at Rockin' Bar D, 12 - 3
Spa reservations - 12 - 3:30.
Kid's club/lab registration - opens at noon
Flounder's reef - 12:30 - 3:15
Common grounds - 12:30 opens
Parrot Cay lunch 12 - 2; Topsiders 12 - 3:30
Changes in dining assignments - noon - 3:30 at Sessions
Shore Excursion drop off - noon - 10 pm
You can make reservations after the safety drill as well, but these are the initial times.
We boarded at about 12:10, did Palo, Spa, then ate lunch, then registered the kids. We prebooked excursions by phone at the 60 day mark.