Guatemala City is the capital of the country Guatemala.
West towards Antigua or the Highlands (Panajachel, Quetzaltengo (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 Antigua, Quetzaltenengo (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 supermarket 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.
A further option is to head to Calle 41, the departure point for highlands-bound buses, and ask for buses to Chimaltenango (Chimal). These buses can drop you either at Chimal (for around 10Q) or at San Bartolomé Milpas Altas (for 5Q). From San Bartolomé, hitching is easy in the direction of Quetzaltenango, Antigua, or Lake Atitlán.
Northeast towards Puerto Barrios, Rio Dulce, Peten, and Honduras
From Parque Colón in Zona 1 (several blocks east of the Plaza de la Constitución on 8 Calle) you can catch the Transurbano bus route 312 that goes down highway CA-9 to El Chato. The stop is on the southern side of the Parque/Plaza, on 9a Calle, with arrivals and departures from a central platform with marked stops for different routes.
Guatemala City sprawls out along CA-9 for a considerable distance from the centre, and so you would be advised to take it a ways out - just leaving the centre you'll be on the edge of Zona 18, a very marginalized area notorious for its insecurity. Anywhere past the Centra Norte mall and bus terminus should be fine - you'll know when you've passed it, as it's the only stop the route makes off of CA-9 before El Chato.
CA-9 is heavily congested until crossing the Puente Belice (Bridge) just before the Centro Comercial Portales. From there onward the traffic flows more easily, and so goes much faster, careening around the sharp curves and winding ascents and descents made necessary by the mountainous terrain. While hitchhiking on the highway itself is possible, and further on is almost the only option due to lighter traffic, finding a spot with terrain and neighbourhood in your favour just leaving the city can be a bit trickier.
No need to worry, as there are several gas stations where you can easily ask for a ride. A couple of kilometers past Centra Norte there is a large Shell station (14.650175, -90.431310), and a good ways further from there (6km) there is a Puma station (14.687692, -90.400672) in Llano Largo, one of if not the last stop before El Chato. Movethathoof got off at that Puma station and secured a ride from the first person he asked, parked at the station's convenience store.
Note: Transurbano buses do not accept cash payment, only payment by the local stored value card SIGA (unlike the Transmetro rapid buses that also serve the city, which have stations and accept cash payment). This is in part because the buses are controlled access (in part as a security measure): there is a gated turnstile that will only allow entrance with payment by a SIGA card (also to be aware of if you're carrying lots of things or have an especially gigantic backpack!). If you will already be using the Transmetro buses you'll need to get a SIGA card, but otherwise you can just ask another passenger boarding if they can pay using their card, and then you give them the equivalent in cash; most people will be only to willing (in the experience of Movethathoof, someone kindly paid for him and then refused to take his cash payment!).
Southeast Towards El Salvador
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.