Most everyone stays in West Yellowstone. However I vote for the Old Faithful Inn.
It sits right beside the old faithful geyser. This is the lodge that Disney used as the model when it designed the Wilderness lodge. Nothing beats the real thing.
At least stay at one of the places inside the park if you can get a reservation.
http://www.yellowstone-reservations.com/lodging.htm
I have never flown in. Always drove. You need a car to really enjoy the park. One good strategy if you have a few days is to spend a night or 2 in the Roosevelt Lodge or cabins. Not glamorous but lots to do on that side of the park. I had the most wonderful fresh trout in the Roosevelt dining Room for lunch last time I was in the park. Most visitors don’t have any concept of how huge Yellowstone Park is. You can circle it in a day. You need a week to experience it fully. Be sure to get off the main road and wade in the river. Sulfur smells like rotten eggs. Ask the kids if they can guess the smell. If you pay attention you will see lots of animals. Please believe the rangers. Don’t try to feed or pet them. They really will attack. Have fun. It is one of my favorite places in America.