Grants sprawls more than its current population would suggest. It's not large, but many of the motels are near the Interstate and fairly far out of downtown, such as it is. As such, driving or cycling are the preferred modes of transport. A bike is handy for around town, but a car is a must for getting to the various nearby attractions.
Public transport in the form of a local bus line is available; call the Grants/Cibola County Chamber of Commerce at 505-287-4608 for more information. Schedules tend to be irregular. No taxi services exist in the city.