Im going to give you my biased answer. Midtown. Specifically the Historic Districts in Midtown. Here is a link to the Historic Society for Mobile. http://www.mobilehd.org/. If you are going to invest in Midtown, you need an agent or broker who knows this area real well. One street in the wrong direction and your investment could be a bad one. I'd recommend you contact Dale Mims, with Mims Realty. His office is right on Government Street next the Downtown. He has lived there his whole life and knows the area better than anyone I have yet to meet. He has represented us in buying many properties in Midtown.
Here is his contact information:
Agent Cell: 251-423-4884
Feel free to contact me if you need further guidance.