I think we have crime for sure like anywhere else but I've lived here for almost 3.5 years now and have never had any concerns for safety! Ive lived kind of all on each side of the "perimeter" of Raleigh, but some of the more popular areas are like Cary and North Hills but they can be more on the expensive side in terms of housing/rent. If you want a bit more of a commute but generally cheaper rent people will live in Apex or Garner areas. I know some people who live in Durham because that is around 30-40 min from the school but Durham can be on the more expensive side as well depending on where you live. Inside the perimeter of the highway that runs around Raleigh is generally more expensive as you start entering the city limits.
(And when I say expensive I mean for Raleigh, I know other places might be worse in terms of rent and housing costs but from what I was used to where I went to undergrad it was definitely more expensive when I moved here) -- FOR EXAMPLE: (I currently live with two roommates in a three bedroom house with a fenced in backyard and it is a slightly smaller house--for three people and two large dogs, but we pay $2000 total and then utilities on top of that, so I basically pay around $750 every month.) But the little neighborhood we live in is right outside of the perimeter and super close to NCSU and soooooo many families and kid's walk to the bus every morning and me and my roommate feel totally comfortable walking out dogs later at night and everything! 🙂
I would definitely say Raleigh is kid friendly, there's a lot of walking trails and there is an art museum with an outside exhibit area that people are always at with their families and they'll have live music, picnics, etc. I spend a lot of time with friends at brunch or dog parks and people are always bringing their kids and having a good time. I can't really speak much more to kids though as I have none lol.
Lol sorry that was so long, let me know if you have any more questions!