I booked a hotel 2 hours from YNP,
2 hours as advertised, or 2 hours as someone real experience? The traffic can be quite horrible at times. Not at 3am, but still.... If there's bear/bison/elk/squirrel/anything interesting by the road (during the day), estimate about 2mph average speed for couple miles.
For my trip, initially I booked a hotel ~1 hour away, just to get something as everything inside YNP were fully booked. Then I planned calling in every few days to check if the lodge by the Old Faithful would have cancellations. I think on my second call there was cancellation, and I was able to get the lodge cabin for less than I would have been paying for the lousy inn 1 hour away.
And if that would give you (me) 1 hour more sleep every morning, I'd be happy paying way more for that.
Especially, do you really want to wake up your wife 3am every morning? I know, people should think twice before marrying a photog, I tried to warn my wife but since when she listened to me. But waking up 3am doesn't sound vacation to me. If I go sleep after that, sounds more like my kind of vacation.