Nuestra Señora de La Paz (English: Our Lady of Peace), commonly known as La Paz, is Bolivia's third most-populous city,the seat of the country's government and the capital of La Paz Department. It is located on the western side of Bolivia at an elevation of roughly 3,650 m (11,975 ft) above sea level. It is, de facto, the world's highest administrative capital.
The city sits in a bowl surrounded by the high mountains of the altiplano. As it grew, the city of La Paz climbed the hills, resulting in varying elevations from 3,200 to 4,100 m (10,500 to 13,500 ft). Overlooking the city is towering triple-peaked Illimani, which is always snow-covered and can be seen from several spots of the city, including from the neighboring city of El Alto. As of the 2008 census, the city had a population of 877,363.
South towards Calamarca / Ayo Ayo / Patacamaya / Sica Sica / Caracollo / Cochabamba (via #1 Panamericana and #4 highways)
Hitch the #1 south to Caracollo, then #4 East from there to Cochabamba, more commonly known as "the road to Cochabamba." Get your first ride from the tranca just south of the east end of Avenida Litoral. Ask drivers how to get to Achocalla. On the route to Achocalla, ask to be let off at the tranca near the corner of Avenida Litoral and "the highway to Cochabamba." Start early in the day, as truckers going to Cochabamba leave in the morning.
The above directions as of October, 2018 would appear to make little sense. There is no tranca on the #1 heading south out of La Paz just south of the east end of Avenida Litoral (though many buses display 'ex-tranca' on their windshields). Achocalla is a separate area not on the highway south. The area up to Avenida Litoral is very urban with heavy traffic.
The first tranca heading south is located in Achica Arriba. Lots of cars and some trucks stop there to eat or for repairs, and of course everyone has to slow down. There is also a gas station just further down the road (though not a very busy one). To get there one can get a van heading to Patacamaya - fare should be ~Bs. 3 (though haggling may well start much higher). These run down Highway 1, many originating from La Ceja. You may also flag one down at the intersection of Tihuanacu and Highway 1, just in front of the Teleférico station 6 de Marzo (though the rush of traffic and excess of buses to other destinations there makes getting one in La Ceja advisable).
Alternately, also at the intersection of Tihuanacu and Highway 1 is a parking lot where lots of truckers wait for cargo. If you head there and chat them up - and are fine waiting until they have the cargo to leave - you could easily find a ride. Most have their destination on a sign in their windshield or on a post at their open cargo beds.
West towards Copacabana / Peru
It is quite a long way to exit La Paz in this direction, because you have to cross El Alto as well, which is not reputed to be particularly safe. Below is a combination of buses that works.
First, get to La Ceja in El Alto. You can either take a micro from the city center, or take the red teleferico line until you reach its last stop (2 stops away from the terminal, 1 from the cemetery), go left when you exit the station, and walk 10 minutes past the green-and-white church. You'll know you're there when you see dozens of buses gathering with people shouting directions.
Second, get to "La terminal provincial". Not sure if it is the main terminal of El Alto. What you are really looking for is "the place where the buses to Tiquina are" ("el lugar donde hay los buses para Tiquina"). Ask around. 1 boliviano.
Then, there are two options. You can take a micro to go directly to Batallas (they indicate Tiquina, ask the driver), well out of El Alto in the right direction. Unlike the micros that go to Copacabana from La Paz' cemetery, these won't charge you the whole price to Copacabana for one third of the distance. Alternatively, look for micros going to "San Roque", which appears to be a place at the edge of El Alto. The rough ride will cost you 1.50 bolivianos. Then walk 15 more minutes in the direction of the bus until the road becomes larger. Here is your spot.
Note that on your way to Copacabana, you have to cross a small patch of lake at Tiquina. The ferry costs 2 bolivianos, and it is per person. There's no real way to evade it.
If you want to go to Peru through Desaguadero, you can use blue line of teleferico to get to "Ex-tranca Rio Seco" station in El Alto. From there you need to go back about 800m using Avenida Juan Pablo 2. After that you will find yourself at the small bridge "Puente Rio Seco". At this bridge you can find trufis which go to Laja (where you can get off at the paytool and start hitchhiking) or to Tiawanacu (if you want to see the ruins) and then start hitchhiking just after the entrance to the city. The last one will cost you 10 Bs (about 1,45$).
Places to avoid
Accommodation and Sleep
There are no great places to camp in the metropolis, though stickbugg found Pura Pura of note. No word on what it looks like up close, and if there are any flat spots here, as it is undeveloped primarily because the highways switches back to get from the El Alto highlands to La Paz downtown. Worth your investigation if you're serious.