I live 25 miles south. Information you've been given is accurate. Do not consider living in the city. If you have children, they would do better being taught by a pack of wolves than the Richmond school system. Come to think of it, at least they would learn survival skills...
Hanover would be my first choice for someone moving to the area, then west--Powhatan, Goochland, Amelia counties, and then south and east. Be careful just east of the city, real problems close to the city.
Overall, central Virginia is nice with plenty to do. You are an hour and a half drive to the beach or mountains. Just keep in mind that the democrats took over both houses and the governor's mansion in the last two years and we are rapidly becoming the People's Republic of Virginia comrade.