Nagarkot is a small resort village on the Kathmandu Valley fringe, and the best place to see Mount Everest without taking a trek.  It's a great place for mountain views, especially at sunrise.  There are several good walks around the area.  There is a cheap minibus to the resort from Thamel.

Between October and March you are pretty much guaranteed good mountain views .  During June to September you'll be lucky to get a glimpse through the monsoon clouds.  It is much cooler in Nagarkot than Kathmandu, and in autumn and winter you'll need to wrap up well.  The resort is a bit fragmented due to a proposed army camp that never developed.

You can get there one day, see the views and leave the next morning.  To take in a walk spend another night or two.

Sights in Nagarkot

The only thing to see are the amazing views.  Mount Everest is a dot on the horizon, but the other peaks of Dhaulagiri, Kanchenjunga, Ganesh Himal, Langtang Lirung, Shisha Pangma, Dorje Lakpa and Gauri Shankar are more impressive.  There is a lookout tower reachable in an hours uphill walk that offers 360 degree views.

Activities in Nagarkot

Hiking is the only activity.  A range of walks from 1 hour to 2 days are possible.  The Lonely Planet Nepal has good descriptions and instructions of the walks.

Accommodation in Nagarkot

Nagarkot has a selection of guest houses and hotels, but quality is a little low, but most have great views. Most have a restaurant.

Getting to Nagarkot

In high-season there is a daily tourist minibus from Lekhhnath Marg (north of Thamel) at 13:30.  It returns from Nagarkot at 10:00 from the Galaxy View Tower.  It takes 2 hours and costs NRs325 one way.  Tickets, including returns, can be bought at Wayfarers.  Large packs can go on the roof.

It's possible to get a taxi from Kathmandu, but it'll cost NRs1400 one way.  You can also walk.