Flagstaff is one of the better places to live and raise a family in Arizona (I grew up there). It is small enough that you don't get the pollution, traffic, and crime of a big city, but large enough that you still have a good hospital, nice selection of stores and shops, etc. At 7000 elevation, they have four real seasons with nice cool summers and snow in winter. It is surrounded by National Forest and within a short drive of many National Parks and Monuments.
The university also results in a higher number and quality of educational and cultural events than you would normally find in a town of that size (~50,000). Because of the university and several scientific institutions (like Lowell Observatory and USGS), education is valued more than in most of Arizona (where education is generally considered a threat to tax dollars) and thus the public schools are generally better than the state average (which over all ranks among the lowest in the country).
The worst part of living in Flagstaff is a higher than average cost of living for a town of that size (it is becoming a popular resort/summer home/retirement town) and limited higher income jobs. The best jobs are with the university or WL Gore (makers of GoreTex). However, every business needs accounting, so there must be a fair number of account jobs there.
The racial make-up of the town is mostly anglo with large hispanic and native american groups. There are not large numbers of Asians or American-Americans, but the town (and most of its citizens) has a very laid back easy-going quality and is generally very open to different people, life-styles, cultures, etc. Politically the town leans democratic and there are strong artist, outdoor enthusist and counter-culture communities.
Outside of Flagstaff, the towns with the largest African-American populations are Phoenix and Tucson, but even here, they are a pretty small minority percentage-wise and the majority is Anglo and Hispanic. Flagstaff and Tucson are the towns that tolerate and even celebrate diversity the most. Racism is more prevalent in the smaller rural towns and to a lesser degree in Phoenix, but even here it is probably not as much as some places back east (other than the current flaring tempers caused by the illegal immigration debate).
Phoenix is where the most jobs are (high-tech, construction, medicine, retirement/elderly related). Home prices and cost of living used to be pretty good for a city of this size, but house prices have shot through the roof in the last two years (hard to find a modest family home for less than $200K), but is starting to slow down. Unfortunately the anything-for-a-buck boom town attitude in Phoenix has also resulted in lots of sprawl, congestion, pollution, higher crime, and a strip mall culture with little interest in community, arts, or good public education (in my opinion). Summer are hot (113 today) but the low humidity takes the edge off it.