Instead of staying in Thamel and taking a taxi where they want to go, there is a better way. This info is taken from information in my book, Nepal: A Tourist's Manual, eBook.
First, take a quadrant of the Kathmandu Valley to explore. Changunarayan/Bhaktapur, Kopan, Pharfing, Kirtipur. So book your room online for the first night or two. This usually gets you a free, or reduced, ride from the airport.
Changunarayan is nearby Bhaktapur, an ancient village that will give you more of a 'genuine' feel. Using this example, book your room at Star View Guest House & Retreat Center or another guest house in Changu. There are several things to do, from painting your own thangka to exploring the nearby villages that each have a unique flavor. There are also 2 museums to explore. It's really quiet, too.