Grasses suitable for lawns in New Mexico are divided into two types: cool season grasses, suitable for cooler parts of the state, and warm season grasses, suitable for warmer parts of the state. Because many areas of New Mexico can be arid or semi-arid, selecting the right grass for your purposes may include selecting a type of grass that requires little water.
Kentucky bluegrass is a cold season grass that is best used in cooler parts of New Mexico. Kentucky bluegrass reproduces via rhizomes, and can withstand wear from limited traffic. Depending on your purposes and location, Kentucky bluegrass can often be mixed with other grasses to create a more durable or more drought tolerant lawn.
A number of fine fescues are suitable for cooler parts of New Mexico. Although fine fescues are generall best suited for cool, humid climates, they can do well in cooler parts of New Mexico as long as you water them often. This fine-leafed grass is shade tolerant and low maintenance. Because they are not very tolerant of foot traffic, they aren't usually good in parks and public spaces. However, as a medium to dark green home lawn turf, they can work very well in New Mexico.
Warmer areas of New Mexico need warm season grasses. Buffalograss is a grass native to parts of New Mexico. There are many different varieties of buffalograss, with modern varieties being more dense and attractive than older varieties generally grown for forage. Buffalograss is drought tolerant and requires much less water than other non-native grasses.
Another warm season grass that will grow well in New Mexico is Bermuda grass. Although drought tolerant, Bermuda grass requires more water than buffalograss. Bermuda grass can become invasive. It spreads by both above ground and below ground runners and can take over flower and vegetable gardens without care or a barrier.