We are getting close to leaving for our trip and one of the things I haven't looked into yet is the arrival. We are flying out of LAX to PPT and land at 4:55am (scheduled). What are the options as far as the ferry? I can't seem to find the schedule for it. When is the first ferry out? Is there anything to do to kill time near the airport since we arrive so early?

Also, what options do I have for early check in at the hotel once I get there? I seem to remember they have a couple rooms to relax while your's is getting ready?