Can someone suggest a hotel that is close to the airport in Bangkok? We have a very early flight home and would like to be as close to the airport as possible (without being in a dive, that is). Thanks.

Basically, you have a choice of the Novatel at the airport, or anything else is 20-30 minutes away. When I was in bangkok in November, it never took us more than 30 minutes to or from the airport (Royal Orchid Sheraton), so I would expect that you could get to the airport very early in the morning from almost any hotel in bangkok in 30 minutes. It's probably not worth moving hotels if you are satisfied with where you are staying/

Other than the Novotel at the airport, there's another Novotel about 15 minutes away that's less than half the price (Novotel Bangna).

There are other options as well, but as Kathie says, there's not much traffic to the airport early in the morning, so unless you stay at the airport, there's not much difference in travel time.

stay in the city and get up early...its what i do for 6AM flight...leave hotel about 3:30

Inside the new airport of Bangkok, there are very good rooms called 'day room" in 2nd and 3rd floors with attached bath/toilet, tv, airconditioning, etc..Also that you can choose the room either for 4hrs or 6 hrs or 8 or 10hrs depending on your requirement. It is located at the farther end of the floor and quiet too.
You may try so that you may not have hassels of traffic on the road etc.
Last month i stayed there and it was comfortable.

We've just come back from Auckland, via Bangkok and we too wanted a hotel near the airport. We chose the Magestic Grande Hotel in Sukhumvit Rd, we got a very good rate through www.asiatravel.com in one of their deluxe rooms. It took us 20 minutes to get there, using the toll roads. The hotel was lovely, we received a welcome drink on arrival and departure. The room and the service was fabulous. I can definitely recommend this hotel.

As both Micahel and kathie has said and I will add, if you are arriving very very late and leaving very early then maybe the Novotel Suvarnabhumi might suite, but it is very expensive indeed.
The Novotel Bangna is about 20 minutes away, much cheaper, but a quality Novotel so it's good value.
There are also a few places like Avana which is across the bangna Expressway which are cheaper, in the USD 40 range.
However beyond those constaints of arrival departure for the extra 10, 15 or even 20 minutes if you are already in a hotel in Bangkok it serves little purpose moving closer.
If you are on an early flight like NW 6 am, or even up to 8 am with check in times now it would mean perhaps heading from your Bangkok central hotel anything from 3.30 to 5.40 am, at that time the roads would be quite clear.
During the busy traffic times that would be perhaps a different scenario, but if you were arriving during the day with a day day flight makes sense to stay downtown 'anyway' for that time scale of time in Bangkok, and if you were 'leaving say afternoon' but arriving late previous night still makes sense to go towntown to enjoy half a day in Bangkok.
Sawadee have a good choice if the area

http://www.r24.org/asiaoz.com/bangkok/hotels/

Novotel Bangna though does give you shopping opportunities.