There are public buses connecting Kathmandu and Changunarayan departing every half an hour. On the way to Kathmandu they also pass Bhaktapur . The fare for Bhaktapur-Changunarayan is Rs15 and this part of the road takes less than 30 mins. The fare to Kathmandu-Changunarayan is Rs40
The town itself is not much bigger than 1 renovated street. Although it's quite nice.
The ancient temple of Changu Narayan, . This place has already been mentioned in the 464 AD and the temple is considered as the oldest temple in Nepal. It is dedicated to Lord Vishnu.Rs100(foreigners), Rs20(SAARC citizens). edit
Changu Narayan Museum, (halfway up the hill). This museum is supported by the village people.Rs200. edit
Living Traditions Museum. On the grounds of the temple you can find this small but well maintained museum. It features some photos and utilities of Nepal. The village people don't support this museum.Rs250. edit
There is a trek connecting Changunarayan and Nagarkot, 3-4hrs one way. And it can be done as a round trip, which accordingly takes 6-8hrs. From Changunarayan trek for some 2 hrs to Telkot, from there you can either continue trekking to Nagarkot for about 1.5 hrs or take a public bus there. (Changu Narayan to Telkot part of the trek being more scenic). The route is not marked.