Managua is the capital city of Nicaragua.
It's kind of pain in the ass to hitchhike out of Managua because it's big and the traffic is a chaos. It's recommendable to take a (cheap) bus to a more frequent road leading out of the city.
Take a bus going to Tipitapa (6 Cordobas). There is the Panamericana which leads south to Granada and north to Matagalpa and Esteli. In between Managua and Tipitapa is the National and the International Airport of Nicaragua so if you don't have to go into Managua it's recommendable to take the bus right in front of the airport going to Tipitapa and get a ride there.
Northwest to León
To go in the direction of León, you can take a local bus to Ciudad Sandino. At Ciudad Sandino, the bus turns left off the Nueva Carretera, and that intersection is marked with rumble strips to slow down traffic, making it a decent spot to get a ride.
Public transport is organised with numbers so you definitely have to ask locals which bus to take. It's very cheap (inner city 2,5 Cordobas which is less then 10 US cents)