Invest in Detroit!
There's a lot of misinformation out there about Detroit. There are basically 3 cities here, in terms of real estate. There is downtown, there are the run down neighborhoods, and then there are the neighborhoods on the upswing. Downtown, you can cross off of your list @ $40,000. But with $40,000, you can buy, renovate, and hold or buy, renovate, and flip (turnkey to an investor or to an end user).
Obviously, there are some risks, which can all be mitigated with some due diligence. But the turnaround time on a cash flow or a flip, as well as the returns both short and long, are going to be a lot better than in most cities.
***Tip*** East English Village is a great place to start looking @ that price point.
Other than that little pitch on Detroit, I think you will find that there are plenty of opportunities in your price point in a lot of markets, but will all come with some risk and hard work.
Good luck!