Although you wake up at the crack of dawn to see the moutain range at its clearest, it's well worth the early morning haul to the airport. There are several local airlines that will take you on a small plane on a one hour round trip flight from Kathmandu alongside the Himalayan range to Mt. Everest.
The plane I went on was 8 seats, so everyone got a window. The pilots called the passengers to the cockpit one a a time to take in the entire view.
It's an amazing experience to hear "We are flying at 30,000 feet," and to be able to look out the window and see mountains at the same height.
This is a picture of the Himalayan range from the plane window, with Mt. Everest int he background. It's so tall that the jet stream is blowing snow off the top.