Thanks, everyone. Our 4.5 yr old daughter has been on 44 flights to 6 countries on 3 continents, and she is generally a good traveler.
I think we found a formula to keeping her interested, curious, and happy on these travels. We do our "cultural" sightseeing in the mornings, when she is not tired, and we don't overdo them. And we spend our afternoons doing outdoorsy, and active stuff; like going to parks. She has a scooter that we use to help her not get exhausted. And we take plenty of fun breaks.
Hoping that I'm not jinxing it this time.