From Boudhanath the cost should be around 250 rupees by day. Night time is more expensive. From Thamel, the cost is closer to 500 rupees. These are prices that should get you to Kopan with minimal hassle. You can negotiate with drivers for lower prices, but some will try to renegotiate after you enter the cab if the price is toward the lower.
Taxis are plentiful in Kathmandu.
Visa and Vaccination You will need a valid visa to enter Nepal. This is now available at the airport for a stay of up to two months. It can be extended for up to five months within one calendar year. Please check for special regulations applicable for your country of origin. No special immunization is required, but Tetanus vaccination is strongly recommended.