Originally Posted by
Csfing1
Hope you get your bag in SIN and are able to keep it with you on your return. After you pick up your bag in SIN you probably will have to exit and won't be able get back thru immigration and security until you get a boarding pass which will be about 3 hours before your departure when check in counter opens so you might consider taking taxi into town to look around. Only things open will be hawker centers or food courts and Mustafa Centre on Serangoon Road for shopping, reasonable prices, big like Walmart, good for luggage, electronic accessories (plugs, adapters, earphones, chargers, etc) watches (Casio, Seiko, Citizen, have never priced the expensive ones), souvenirs etc. After midnight there is 50% surcharge on metered taxi fares. Let us know how your trip goes and when you get reunited with your bag.
Happy Travels! 
Cheers!
Ok, I'll give a fairly complete trip report now and update if anything happens on the return. I actually did the MR with one day in Singapore, giving me basically a 30hr layover. NRT-SIN was delayed on Tuesday night, so it wasn't until almost 2am Wednesday that I went through Immigration and got my bag. Everything was fine, but as Csfing1 correctly points out, once I got my bag I had to leave airside. I will make sure I don't let the GA gate check my bag next time, what a hassle.
I went to T3 and used The Haven lounge. It is landside and offers 3 hrs free with Priority Pass (they were fairly strict about the 3 hours - "please check out by 5:15am" ok...). But it included a shower and a meal from their menu. The Thai Curry was quite good. Alcoholic drinks are extra, but there is a good selection of soda, tea, and espresso machine. I would definitely visit this lounge again if I was stuck landside at Changi.
After that, I took Csfing1's recommendation and went to Moustafa Center. Got some cheap souvenirs and snacks to take home (green tea pocky, anyone?). I also went to City Square Mall and had lunch there - the food court is huge. Around noon, I broke down and booked a hotel room nearby, as I was getting very tired.
After a nap, I went to explore Marina Bay. The Sands hotel is impressive, and the attached shopping mall and casino would rival Caesar's Palace in Vegas. When it got dark, I went to explore the Gardens by the Bay. They are really pretty when lit at night and free to the public. I would highly recommend this if you are in town for the evening. Took MRT there, very easy. I forgot the MRT stops at midnight, so I had to take a taxi back into town, but it was a reasonable $8 even with the 50% surcharge.
Getting ready to head back to Changi for the return. I would note that I was able to print a boarding pass at T-24, but the pass specifically says this is not valid for immigration without a DOCS-OK stamp, so I assume it is basically useless for getting back airside. I had wanted to go catch a movie at the Changi Theater, but I'll save that for another MR...