I'm partial to TN, but NC, KY, GA, AL would be next in that particular order. I'd imagine that you'd need to find a larger city to continue as a medical investigator/forensic scientist, your wife's SW position might be easier to place. Absolutely no offense to any members from NJ as it has it's pretty areas, but I'd move ricky-tick out of there. My Yankee wife has settled in wonderfully in TN and she's from Philly PA and loves it here. I'm a purebred TN mutt with roots in this area since 1803, so being back here makes me like the proverbial pig in slop.
UT Knoxville has a leading forensic graduate school, it's the home of Bill Bass from Body Farm fame. Chattanooga has an active regional forensic lab, nice folks that I got to know in college. Memphians are really good at killin one another in interesting ways and they have a large, busy and dedicated lab there. I did some work with them while I was in medical school. I'm sure Nashville also has some good forensic investigators.
If you settle in TN or have some specific questions, go down into the state forums and ask around. We have members spread all over the state if we can help. GA also has an active state group.
As far as hunting, all states are pretty good and have liberal bag limits and the seasons are long. TN and KY have elk. TN/GA/NC have bear. Most states have populations of hogs now, but are certainly thicker in the deep south. I don't know that there is a bad state to hunt in, but you will have to pay attention to cities near public ground, or else consider joining a lease.
Good luck, move while she's motivated, don't look back except for holidays and learn to drink tea the proper way - sweet!
David