We love Anytime Dining! Being able to eat when WE want to and not at a specific time is great! As Kuki said, you may have to wait a few minutes for a table, but not any longer than you'd wait for a land-based restaurant. If you want to eat with others, (we do!) generally, you'll be seated immediately. If you request a 2 top or a 4 top you may have to wait 10-15 minutes. They'll give you a pager and we've found by the time we get back to the bar, it's going off !
BTW, Sun Princess is our favorite ship (so far!). All of the crew seem very happy to be on this ship!
Have a great cruise,
"A truly happy person is one who can enjoy the scenery on a detour."