Guatemala City is the capital of the country Guatemala.
Towards Antigua or the Highlands (Panajachel, Quezaltengo (Xela), El Quiche)
From the city's transport hub Trebol on the Panamericana you can start hitching on one of the service stations or getting farther away from the center by bus or walking. It's not dangerous as there is a lot of traffic and people.
I you are leaving the city via bus the safest bus stop to start your journey out of the city is past Trebol across from the modern shopping mall Tikal Futura. Here you can catch a bus to Antingua, Quezaltenengo (labeled 'Xela' on the buses) or for Panahachel (Pana). At this stop there will be a guy with a clipboard who can help you take a bus that's going your direction.
Another option is to take a bus to San Lucas (it's the same direction as Antigua) and get off in the stop "entrada a Santiago" (you will know where it is as the helper will scream that when you approaching), walk in the direction of the road. There's a petrol station next to a supermaket where you could ask people. Or keep walking in the direction of the road past the bridge, you can start thumbing past the on ramp.
You are in the urban are all the way to the point where the road begins to wind up the mountains. This is a rich and safe neighbourhood. User Worldhitch was waiting quite a lot there and got a ride in a curve on the way up. Going farther up by bus may increase your chances.