Taxis can be expensive, and there is often a fairly long wait for pickup, except at the Sunport. If you want a fixed price and know the rate in advance, you can pre-book a transfer online. Some companies offer these services from Albuquerque Airport to anywhere for individuals and any size of group.

The city is extremely navigable.  Just remember that the Sandia Mountains are in the East, as people asked for directions will often use phrases like "head north on 4th street" or "go east on Montgomery past Louisiana" and you should do fine.  It is best to obtain a rental car, as there is so much to see in, and around the city. 

Albuquerque's city bus lines are quite extensive, and a good choice if you are not traveling a great distance, such as Central Ave. downtown, west to Old Town, at Central and Rio Grande Blvd. You may see a map of Albuquerque's routes, and scheduling at:

The new Alvarado Transportation Center, located at the corner of 1st St. and Central Ave. SW, is the new home for city buses.  It is also adjacent to the Amtrak station, and serves as the departure/arrival point in Albuquerque for interstate bus lines, such as Greyhound.