The larger cities Albuquerque, Las Cruces, Santa Fe have some degree of public transportation, but this is still a state where you'll have to drive most of the time. The New Mexico Rail Runner Express (http://www.nmrailrunner.com) commuter train connects Albuquerque and Santa Fe, along with residential communities in the area.
Roads in New Mexico are generally well maintained and driving itself can be a pleasurable experience. Although only a few roads are designated scenic drives, most rural highways in the western two thirds of the state provide splendid vistas. However, if you are behind the wheel, please remain attentive to the road and the local driving habits. New Mexico has road conditions and situations that may be different than your own; use caution and drive defensively at all times. Speed limits on interstates are normally 75 miles per hour, except in urban and mountainous areas areas where the speed limit typically drops to 65. Multilane US and state highways have rural speed limits ranging from 45 to 75 miles per hour. Two-lane rural highways have speed limits in the range of 45-65 miles per hour. In urban areas and other communities speed limits can be as low as 15 and as fast as 55 miles per hour, and enforcement is more highly visible and heavy-handed than in rural areas. A number of state highways and most county roads, remarkably enough, are still unpaved and should be driven at reduced speeds. Between this, a number of radar traps, and the fact that many of the roads through the mountains are more sinuous than is apparent on a map, you should expect intercity travel to take a bit longer than the distance would imply, except on the Interstates. There are exceptions in the eastern parts of the state, where you're in serious danger of being run over if you drive as slowly as the speed limits.
Weather-related driving hazards are generally confined to the winter months, when the northern half of the state, as well as the mountainous parts of the southwestern region, can experience snowstorms that close highways or render them hazardous. Have chains or 4-wheel drive available in these areas from December through February, particularly in the mountains. Spring winds can be disconcerting to drivers in tall vehicles and occasionally create reduced visibility from blowing dust, but dust storms are less of a problem than in some neighboring states. Most of New Mexico is at higher elevation, hence slightly cooler, than other states of the Southwest; problems with boiling radiators, etc., are therefore not as common, although it's still a good idea to take water with you when driving in the summer, particularly along the low, hot southern tier I-10 and vicinity.
New Mexico has a severe problem with drunk driving, although aggressive enforcement and public-education campaigns have reduced DUI levels somewhat, compared to 10 years ago. No road in the state is immune to this problem; there is no time of day when it cannot occur. Defensive driving is the obvious antidote. Large animals on the roadway create hazards as well. Cattle and sheep are often seen in the open range areas of the state; elk are seen in the north central mountains. In the south, the Oryx, an elk-sized antelope imported from Africa, or the Javelina aka the Collared Peccary, a distant relative of the pig family, are often seen on roads, especially rural routes. Again, just drive defensively.