There are some good options from Kathmandu for day hikes around the rim of the Kathmandu valley with great views of the Himalayas to the north.
Nagarkot to Changu Narayan
Nagarkot, 2125 metres, is situated 32 km on a ridge above Kathmandu with fascinating views of the high Himalaya. The long chain of peaks extends from the Dhaulagiri and Annapurna ranges in the west to Everest in the far east. If you have only one day to spare you should leave your hotel in Kathmandu in the early morning say around 4.30 am if possible and drive to Nagarkot to see the spectacular sunrise. After the sunrise and a good breakfast at one of the beautiful garden resorts of Nagarkot start your walk down to Changu Narayan temple.
Changu Narayan is a World Heritage Site and is one of the finest pieces of temple architecture in Nepal. The temple was damaged in the current earthquake but efforts are underway to re-build the temple as it was. The walk down would take around four hours or so and follows fields and terraced farmland with spectacular views of the Kathmandu valley and the peaks of the Langtang and Ganesh Himal group. Late autumn and winter is an ideal time for this walk with the warm winter sunshine and mellow colours giving a lot of photography opportunities on the way. From Changu Narayan you could take a taxi back to Kathmandu and also visit the heritage site of Bhaktapur on the way.
Nagarkot to Dhulikhel
The five hour walk from to Dhulikhel (1550 metres) is through scenic forests with the Langtang peaks, Ganesh and Jugal Himal in full view on a clear day. Terraced farmland, small villages and rustic trails offer a glimpse into rural Nepal which is not usually seen by visitors. . Dhulikhel also has a spectacular view and has many traditional Newari houses with old temples and stupas. From Dhulikel you could take a taxi or bus back to Kathmandu.
Kathmandu Valley to the Shivapuri Ridge
Situated north of Kathmandu valley, Shivapuri National Park and the ridge offers a good day hike through forested paths. Take a bus or taxi to Buddhanilkantha which would take around 30 minutes, You can see the reclining Vishnu here which is definitely worth a visit.
After this start the 15 km walk to Shivapuri. Register at the park gate and pay the fees Rs 250 for foreign tourists and then climb up to the ridge on top through dense forests - the flora and fauna in this park is amazing. If you want you could walk back to Kathmandu or take a bus down to the valley.