Depends on your energy level, but if you want some decent rest I'd suggest the transit hotel over the lounge Obviously nothing fancy, but perfectly adequate and convenient and fairly quiet. You don't have to clear immigration/customs to access it. Do book ahead, though, as they sometimes are full if folks simply show up expecting a room.

Personally, I don't find the hawker centers or Little India so enticing that they are worth more than an hour for a meal in the middle of the night...I wouldn't say Little India is all that enticing even during the day, as it's a somewhat run-down (but safe) part of town.

If you do head into town, find out in advance from the collective wisdom here or elsewhere whether you can count on easily finding a taxi back. At one hawker center we visited earlier this year, finding a taxi was an issue.