AD Design pretty much covered it. If you want to work in the south then look where TN, GA, AL, SC, NC all connect. It's a melting pot of large and small shops in that area. Most are maintenance type shops supporting the larger factories so it can go from a 4 day week to 7 days+ real fast. If you have good organizational skills you can walk into most anywhere as a setup guy between $15-$20 and hour. That's a decent wage for the area as the cost of living is quite low. Tennessee has no state tax so that's a nice bonus.
A lot of the gravy train machinist jobs you may as well forget about. M&M Mars, Olin Chlor Alkali, Bowater Paper, Dupont, and several others all have beautiful maintenance shops but they contract everything out to local job shops. They all have machinist that don't do anything but sketchup a broken part then send it out, or just send the broken part and let it be someone else's problem.
There's a lot of shops in Chattanooga but that town has spent the last 20 years trying to recover from a union strike at ABB Combustion Engineering when 350+ Machinist at $60 an hour decided they wanted more benefits. Combustion gave em all the one finger wave and closed the machining areas. It was a great time to own a machine shop in that area in 2000. They had an auction that was not advertised more than a few cities away. Pretty much whoever bought a machine at the auction got the job that the machine did so long as they didn't hire one of the former union machinist. It was a hush hush deal but the whole town knew they were blackballing those union workers.
The problem now is Alstom bought out ABB and put in a huge turbine manufacturing plant and had a few hundred machinist knocking down $75 an hour up until recently Then GE bought Alstom out and closed it again. Now the towns flooded with highly skilled guys fighting for $30 an hour positions at the job shops only to find they can't handle the fast paced work. For shop owners its a total cluster fk trying to get a good job shop machinist or "Out of the box thinker" because of all the ABB/Alstom guys.
If I was back in the states Chattanooga would be more of a last resort. 20 minutes north is Cleveland and probably 15-20 mom and pop shops. Cheap cost of living and great little town just make sure your right with god or you'll get a southern Baptist Scolding. Then you got Athens TN, another 20 minutes north with probably 40 shops supplying automotive interior tooling. But the place is the Meth capital of Tennessee.
Another 20 minutes north you have Knoxville witch is booming with shops but the cost of living is a bit high. Nashville's nice if you want to be around middle Tennessee but the crime rate would deter me. As AD said "Memphis" but I as well don't have any desire to even visit that town.
Huntsville is right on the TN,GA border and if you’re into Aerospace then that's the place to be. With NASA/Redstone Arsenal there it draws in every Aerospace company imaginable. Great place, low cost of living, plenty of work, half a day to Gulf Shores Alabama beaches and just a few more to New Orleans. BUT,,,, It is the most racially divided city i've ever been to.
Head back east a bit into GA and Atlanta is a booming city. Loads of shops to choose from and lots of stuff to do. Six flags amusement park for the family then another half dozen water parks. If you like guns about 15 minutes north of Atlanta is Kennesaw GA. Great place to live if you like guns as "every head of household residing in the city limits is required to maintain a firearm."
Then you go a bit more to the South East and you get Savannah GA. By far the best place I ever worked and lived. Home of Gulfstream Aircraft and probably 50+ Suppliers for them alone. Then there is 2 of the largest Nuke/Fossil plant repair shops in the states next door to each other. Then JCB Heavy Equipment, Hobart, Georgia Pacific, ADM Milling. The shops there throw $$$$ at you. The whole town is one big party and everyone in the manufacturing areas know everyone. It's not long before other shops start trying to snake you away from where you’re at.
There is plenty of opportunity in the South East. Just pick a spot that looks nice to you and pop a resume out.