Langtang
The closest big mountains to Kathmandu, and the quietest of the three main regions.
Langtang is a few hours' drive from Kathmandu rather than a flight, which makes it the best option when time is short or when the Lukla weather is being difficult.
A steep, forested valley that opens out into yak pasture with Langtang Lirung above it, and the Tamang villages of Kyanjin Gompa at the head. There is a day-walk up Tserko Ri for a Himalayan panorama that costs a fraction of the effort the same view demands elsewhere.
The valley was hit hard by the 2015 earthquake and has been rebuilt by the people who live there. Trekking here puts money directly into that recovery, which is a good enough reason on its own.
Autumn and spring are best; winter is walkable lower down and beautifully quiet.