Head into the city. Hang out around the Galle Face Green (and beach - well sort of) - do lunch and drinks at the Galle Face Hotel.

Get a quick TukTuk tour of the main attractions and temples - not that much to see

If your staying the night why not do it at the Galle Face Hotel - one of the oldest and grandest hotels in Asia.

FYI. Also caught the CMB-HKG flight at 1am (but only after a 12hr layover) in April this year. Check-in only opened about 2.5hrs before the flight.... There is nothing to do in the departures (although it was being renovated while I was there) - you can access the single canteen (post security) by going up the fire stairs to the upper level.

Once checked in and into the terminal proper the offerings are quite reasonable - a number of food outlets still open at that hour. The OW affiliated lounges (unsure if you have status) in the new wing are very good although no showers -- Showers are available on the right just after you enter the departures terminal -- they only accept USD - $3/4 from memory. [Luckily despite being an Aussie I always carry some USD on my travels].

Also if you're wanting to store baggage while hanging around for 36hr the Baggage Storage office is outside the airport on the main road... Be warned when you leave the terminal after arriving - it will be an absolute madhouse out there!