Singapore is great, my favorite place to get stuck at in Asia. It is like an Asian starter kit and it has a mesh of just about every culture, SE Asian, Chinese, India, Western world. You won't have any trouble finding something to do, or eat. You can eat everything there and not get sick, even street food. Most everything you eat, even if it costs $2 is amazing, especially food courts. Do you know where you will be staying? Are you going to be staying on Orchard Blvd? If so, just walk around, you'll never get bored. Try an ice cream sandwich. Its just ice cream on white bread but it is actually pretty good.
You are not taking a normal trip so I don't know what your access to the airport is going to be, but the airport alone is amazing, world class shopping at fair prices. It has an amazing food court and other food places, a movie theater, work out facility, massages, scenic fountains and lights ect. ect. Nothing in Sinapore is half assed. My favorite place to eat at the airport is at Sushi Taco. I think they have a location in the city as well. Google and see, but check out the owner, she is so hot.
You can search and find a million attractions and highlights of places to go and things to do. Anthony Bourdain and Andrew Zimmern all have shows on Sinapore and are worth watching, just youtube them. Singapore is only like 24 miles long and 12 miles wide. You can hit tourist places as well as obscure places with ease.
If I had to pick one thing, You should not leave there without going to Marina Bay hotel (the boat hotel). I might be wrong on the floors, but you can go to the 26 floor for free and visit the bar and look at eye candy at the infinity pool and watch an amazing sunset. Plenty of high class tail. You can pay around $20 and go to the 25th floor and swim in the infinity pool.... highly recommended. Go swim in the pool in the afternoon, change into some clothes for sunset and visit the bar for a few drinks. After dark walk right behind the hotel and go through the walk park and walking bridge and look at the lights. Its an amazing place.
Universal studios is awesome as well. Wear some shorts so you can take a break and hang out on the beach while there.
Just from being there a lot, I can tell you that Sundays are free house maid day. All the Indonesian house maids are off from work and the women out number the guys about 500 to 1 on the street. Or you could just go to the 4 floors of whores, have some drinks and see where Sincity leads ya. lol.
Singapore is a "FINE" city. Don't chew gum, eat or drink anything on the metro. Don't chew snuff and spit on the street or bushes. You will hardly ever see a policeman but they see you always on CCV and the fines are stiff. Don't be a dumb ass and do anything stupid, you are always being watched. But, it is a safe place to be. You have to be the biggest Moran in the world to even think about drugs in Singapore, but you are a servicemen so I get that won't be a problem.
If you are jet lagged, there is a really cool movie theater on Orchard Blvd that is open through out the night that seats 810 people. I've been there at 2 AM with only 30 or so other people watching. It was kind of cool and I try to put it on my list of things to do.
I'm Catholic, so I like to go to church while there. There are 2 Catholic churches there that are architecturally amazing. like going to church at the Vatican kind of architecture with English Mass.
I love Singapore. I believe I will be going there sometime in January. When are you going to be there?