Several people approached us to guide us around the city but they didn't pester us or follow us around. Prices vary a lot for these unofficial guides and the price can surely be negotiated. I wouldn't trust the people who say they would guide you for free, as they'll probably request some payment at the end. We preferred to explore at our leisure and enjoy the small, empty streets at our own pace. The guides said a tour took at least an hour and a half, and that's about as much time as it took us to walk around at a leisurely pace. Unfortunately, the weather conditions that led to the cancellation of our morning flight caught up with us and as the rain started, we decided to stop for lunch at a restaurant perched at the top of a building just off Durbar Square with an unbeatable view and proceeded to order way too much food for 2 people.
Airport - Thamel area: Rps.700 ( about US$7)
Kathmandu - Bhaktapur - Nagarkot: Rps. 2200-2500 (about US$22-$25)
Bhaktapur entrance fee: Rps. 1500 (about US$15)