Eastwood was drafted in the fifth Round, 91st overall by the Toronto Maple Leafs in the 1987 NHL Entry Draft. He then played four seasons with Western Michigan University of the CCHA. He played 164 games for Western Michigan, scoring 69 goals and adding 80 assists for 149 points. His best season was his last one when he had 29 goals and 32 assists in 42 games. In 1991, Eastwood made the jump to pro hockey. He did not become an NHL regular though until two years later.