@Eric Rice Maybe I am too dense but I read your post a few times and I am missing the separation of where you want to live and what you want for investing.
I mentor people who want to invest in residential real estate to generate cash flow. From LA (I am in San Diego), to get good performance of the investment, I recommend to turn the invests you are willing to make into a small business. (I can expand more about it you are interested).
You or your wife can run it and have all the benefits of real estate investing. Your post seems to indicate that you like to develop a passive income portfolio. That's exactly what we do using 1% and 2% properties in well-performing markets.
Running it as a business means you hire all the needed services. You have property management, insurance, loans/mortgages from banks and lenders, you and tax person, and maybe someone like me who provides you with already vetted deals from trusted providers.
Yu can get some mid-size deals that maybe pay $300/month or less financed deals that pay about $800/month.
All this and a lot more details I am happy to discuss with you and your wife is related to your investing business.
Independent of that should be where you want to live. That's where your list comes in. The only connection I see is the initial cost of the place you get in your new location.
If you move to Austin I would rent right now. The other two locations you could buy a nice place with a regular mortgage. If you or your wife are eligible for VA, even better.
The investing is separate from the place you live.
I live in San Diego and in Spain and my investments are in the Midwest.
The main reason is the performance of the investments - basically the balance of purchase price and rent income.
If your investing goals change to something else, i.e, appreciation, the situation is totally different.