If you aren't gong to stay in the airport transit hotel (and with 12 hours, I agree, don't do it), stay in the city. Several years ago, we stayed at the Le Meridien Changi Village, which is billed as an airport hotel. It took about the same amount to time to get there from the airport as it would have to get into the city. The way back to the airport was shorter than staying in the city, but since we're talking bout a 20ish minute cab ride from the city, it wasn't worth it to me to stay at such an inconvenient location.

http://nof.ywca.org.sg/index.php?option=com_content&task=view&id=58&Itemid=205 is in a handy area near the river and plenty of eateries along the river and not sure if the parkland kiosks still exist but food there too.
The famous Raffles Hotel is nearby if you want a look and to see whether all the peanut shells still litter the Long Bar on upper floor to the extent they cascade down the stairs.

I used to stay at the Changi Village ( old Le Meridien ), like Kathie mentioned it is not so close to the airport, the only good thing was the free shuttle and in the mornings it certainly was easier to get to the terminals.
There is the Crowne Plaza which is right at the airport.

Question: Are you by chance flying with Singapore Airlines , if so their stopover deal could be interesting.

If you are arriving early evening and fly out next morning it's really an open choice if you use cabs to/from, in that case choose somewhere to overnight that suits you.

Or, stay at Crowne Plaza and then from there head to a restaurant, then back to Crowne Plaza and you are 'right there' for your morning departure.

Has anyone actually stayed at the airport Crowne Plaza? It's certainly convenient, but that decorative lattice work on the facade is so strange. I've wondered what it's like from inside looking out.