When driving in outlying areas, be careful to avoid hitting deer. Keep in mind that most such accidents occur at dusk, and that deer usually travel in groups of two or more-- so if you see one, be aware that another may be nearby.
US Rt. 90 from Silver City south (toward Lordsburg) is especially prone to deer encounters for the first 20 miles or so.
Silver City is not crime-free (what place is?). Like much of New Mexico, Silver City's crimes are generally alcohol- or drug-fueled: drunk driving, domestic violence, vandalism, etc. The cops are friendly and professional and are trying to keep the lid on.
Like many places in the Western US, Silver City's gentle climate draws its share of panhandlers, especially in the warmer months. While this sentiment is by no means unanimous, many residents feel that it is counterproductive to provide panhandlers with money, as it frequently is used to support the recipient's alcohol and/or drug habit.
Driving in Silver City has become a bit hazzardous because of the infrastucture. Silver City has grown over the years and the roads do become crowed on the main throughfares. Times to aviod traffic are 8:00 AM to 9:30 AM, 11:30 AM to 12:30 PM and 3:00 PM to 5:00PM.
The dwellings are at something like 8000ft. elevation and it is all uphill to get to them, so don't expect and easy stroll.