Mexico City is a huge place, but driving is definitely not a way to see it even if tourist attractions are scattered throughout the city.
A good way to plan your trip is to stop by Guia Roji to identify the location of the "Colonias" (neighborhoods) you intend to visit. You may also try Google Maps and Map24 to find addresses and even look for directions.
Mexico City has several public transport alternatives. Metro is reliable and runs underground, the city government operates the RTP bus system and Electric Trolley buses. There are also plenty of franchised private buses which are less reliable and safe because of their driving habits. And finally thousands of taxis, many of them old Volkswagen bugs in their famous green paint scheme and called verditos, or little green ones.
Get around Mexico:
1) By metrobus
Mexico City MetrobusEstablished in June 2005, the Metrobús operates in a confined lane along Insurgentes Avenue. Plans exist for additional routes. It costs 4.5 pesos to ride during the day, but a card must be bought in advance (11 pesos). After 11:30 or so, it's 5 pesos. There are stops approximately every 500m. Expect it to be crowded around the clock, but its a great way to get up and down this major thoroughfare.
2) By trolley bus
"Trolebuses" are operated by the Electric Transport Services. There are 15 Trolley bus lines that spread around for more than 400 km. They usually do not get as crowded as regular buses, and they are quite comfortable and reliable. They can be a little slower than regular buses, since they are unable to change lanes as quickly. There is a flat fare of 2 pesos, and bus drivers do not give out change.
3) By light rail
The Tren Ligero is operated by Electric Transport Services and consists of one single line that runs south of the city, connecting with Metro station Tasqueña (Line 2, blue; alternatively you may see it spelled as Taxqueña). For tourists, it is useful if you plan to visit Xochimilco or the Azteca stadium. The rate for a single ride is 2 pesos, and while the ticketing system works very similarly to the Metro, the tickets are not the same. You must purchase light rail tickets separately; they are sold at most stations along the line.
4) By taxi
There are more than 250 thousand registered cabs in the city and they are one of the most efficient ways to get around. The prices are low, a fixed fee of about 6 pesos to get into the cab, and about 0.7 pesos per quarter kilometer or 45 seconds thereafter, for the normal taxis (taxi libre).
Note: If you get lost:
If you get absolutely lost and you are far away from your hostel, hop into a pesero (mini bus) or bus that takes you to a Metro station most of them do. Look for the sign with the stylized metro "M" in the front window. From there and using the wall maps you can get back to a more familiar place.
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Based on a work at Wikitravel.org & Traveldudes.org.