For anyone else needing input, here was my experience.

I could not find a reliable answer to whether or not I could sleep at the airport. You most definitely can, I learned on arrival.

Not knowing that, I booked a cheap hotel (Giang Thanh Hotel & Apartment Lodging via http://hotels-in-vietnam.com). The room was about $25 and I paid about $20 for their transfer to the hotel (I know I way overpaid - but I wanted the convenience of coming out to my name on a sign, not changing any local money, and the risk/hassle of explaining to a taxi driver where I needed to go and hoping we went straight there).

I would not use the hotel again. It was fine for the price paid. It was not buggy or scary - but the sheets were not clean (a good number of hairs - but they didn't look slept in), and they have no "desk". A night security guard let me in and spoke no English - so I had no way back to the airport in the morning. I had to walk.

Thankfully I'd chosen the Giang Thanh because it was very close to the airport - so I just walked. It did not feel unsafe to do so, and it was quite busy on the street when I got up at 5 to make the trek.

So to stay on topic of the thread - I would say there's nothing wrong with the Giang Thanh, but I would not stay there again if I needed a cheap place near the airport. There were dozens of options to choose from online.