You can get an airport hotel at either place that has a shuttle, but I don't know of places that have a shuttle to/from both airports. If I understand you correctly, you get in early one morning and leave early the next morning. You'll have a whole day to spend in Bangkok. Given that, I'd choose a hotel in the city close to what you want to do/see that day. Taxis are cheap, about 350 baht each way plus any tolls.

Suvarnabumi is northeast of the city and Don Muang is southeast of the city. As Kathie says, you can stay at one airport or the other. At Don Muang, the Amari Hotel is attached to the airport via a bridge - very convenient. You can book it inexpensively on asiarooms.com. That being said, if you have a full day to kill in between flights, use taxis and stay in Bangkok. If your budget permits, stay in one of the riverside hotels located on the east side: the Peninsula, the Millennium Hilton or the Anantara.

Craig, I think the airport locations are the opposite, DM is NE and Suvarnabumi SE. I'm booked on an Air Asia flight and was just checking on their move from the new airport back to the old one.

Here's information on transport means & times between the 2:
http://www.airasia.com/my/en/latestnews/bangkok-move-don-mueang-airport.page

Mme, you are correct.

craig was standing on his head when he wrote that...

i would vot for an intown hotel too and/or the amari at DM---its very cheap now

(but the Amari at Don Muang is just awful!)

At US$40-50 how bad can it be, Kathie? Remember when it was 4x that much?
And yes, Bob - I was upside down or at least looking at the wrong map...

It was pretty bad when I stayed there. The carpet was so dirty that I hesitated before walking barefoot on it. And remember how there is a sill when you come out of the bathroom - I could just imagine tripping on it in a half-asleep state.

Besides, if you have a whole day in Bangkok take advantage of it. Stay in the city even if all you do is get a massage watch the ever-fascinating river traffic and have a nice dinner.

Choose a hotel in the city so you can walk to restaurants, malls, street vendors, etc. There are even hotels that are near the Skytrain route too.
http://www.urbanrail.net/as/bang/bangkok.htm

Millions of tourists use taxis from the airport to city hotels every year. There is also limo service from the airport too. Your hotel can also provide transportation if you prefer.

Meter taxi to Siam area or Sukhumvit Road area roughly around 340 - 390 baht which includes meter fare to hotel and 50 baht surcharge (both paid at hotel) and probably 2 toll charges coming to 70 baht. You pay the tolls during the ride. Have small bills to pay taxi drivers, don't expect them to have change for a 500 baht note.
http://www.bangkokairportonline.com/node/52

The fare for a meter taxi in Bangkok is for everyone in it not per person! In the city using the meter is cheaper than bargaining the fare. In the city have coins to for paying taxi rides. No problem getting a meter taxi to the airport all night long. If you want your hotel can also provide transportation to the airport too.

Up to you.

OK, you have convinced me! NOW, what hotel would u recommend???

I'd recommend one of the hotels on the river: Pen, Hilton, Anantara, Royal Orchid, Oriental, Shangri-La or Chatrium.