As you face the check in desk, there's a diamond check in office way off to the left. You want to go that way.

I don't think time of day matters all that much. Housekeeping will do all the rooms of checkouts first, and then do all the rooms of people staying (assuming they are all empty) and unless you are checking in at 10 am, there will probably be a room. What will matter is if it's your first time there or not, as they treat repeat visitors much better than first timers.