Most hiking the Everest region in Nepal fly into and/or out of Lukla, a small village at 2,860 metres (9,383 ft).
You can walk in and/or out, but that requires a lot more time.

In order to ease congestion at Tribhuvan International Airport (in Kathmandu) and facilitate ongoing runway repair works … Lukla flights were rerouted to fly from Manthali.
An airport that had barely seen a dozen flights in the last decade began to handle 85 flights daily, and it was ill-equipped to deal with the hundreds of tourists arriving daily. The airport lacks proper parking, a waiting room, toilets and even a restaurant.
More than 800 tourists arrive and depart daily during peak season. About 85 flights a day.
For Everest enthusiasts, an unpleasant experience awaits at Manthali airport (Nov 15, 2019)
It’s 132km (82mi) from Thamel, Kathmandu to the airport. That’s at least a a four-hour drive IF there are no delays. You leave Kathmandu around 2am.
Know that there are still a couple of Lukla flights departing Kathmandu airport after 8am each day. But it’s risky to buy that ticket as your flight might be cancelled.
Flights out of Ramechhap airport at Manthali — however — are shorter, cheaper and more reliably get you to Lukla.
The international airport in Kathmandu is terrible. Current renovations won’t help much.
The planned (2025) replacement will be situated 150kms from Kathmandu by road.
Two other new airports already under construction should help relieve traffic: Pokhara International Airport (opening 2021) and Gautam Buddha Airport. (opening 2020) should help.
I’ll try to fly into Pokhara in future. We should avoid polluted Kathmandu, if we can.