I graduated from Fayetteville in the mid-90s, and have been there on a number of occasions since then. I say that simply to point out that I have some familiarity with Fayetteville, the surrounding area, etc. In all fairness, though, I did not realize that it was 70K+ people. Fayetteville has many fine qualities, but . . . like any college town, there is a transient population of young, alcohol- or drug-imbibing folks, and there's a new crop of them every fall. The overwhelming majority of them are harmless, I'm sure. A few of them are not, however. What's more, they provide a market for certain illegal items and activities and the providers of those items and activities may not be transient.
I'll also say that pax's site (the cornered cat) is a really good resource. However, once you've read it, I think the key will be getting your wife to read it. There's an awful lot of good information on their about dealing with the issue of guns and kids.
Maybe I missed it, but exactly what is her objection? Simply that you don't need to carry? I sincerely hope she's right. I hope you never, ever need to draw your gun in SD. Not to beat a cliche to death, but bad guys don't make appointments.
Registered sex offenders are a problem, but IMO, the real problem is the unregistered ones. The ones who have either moved from their old address and not registered, or simply never been caught. There are also a great many criminal activities that do not require that one's name be put on a registry. After all, when was the last time you heard about someone being put on a registry for first-degree battery, or armed robbery?
I'm a lawyer, but I'm not your lawyer. If you need some honest-to-goodness legal advice, go buy some.