You can get to Chinandega from Managua on a mini bus or bus in Huembes Market. This costs $3 and takes 2.5 hours and is very safe.
You can also get a mini bus collectivo from Leon terminal to Chinandega terminal every 15 minutes. This costs 23 cordobas 1$, and takes about an hour.
Hitchiking is an option, as is renting a car.
Chinandega is past Leon. Refer to ViaNica for more directions (http://www.vianica.com)