Detroit neighborhoods are many, it would depend on the size and style of home that you would like and the type of amenities you would like to support your life style. For more detail info please contact me.
Some areas that you might want to check out are Sterling, Utica, Southfield, and Northville if you're into outer-ring areas. You might want to check out Dearborn if you're more into inner-ring areas. You might also want to check out some of the down-river suburbs too; Monroe is nice (and it's the home of La-Z-Boy).
Unfortunately, this is a question that cannot be answered by a real estate professional because of "Steering" laws and fair housing.
What we can do is direct you to a resource where you can find the information for yourself, and that would be the Detroit Police Department. That information is public knowledge and they will disclose it to you. In fact, a quick google search will give you this link: https://www.detroitmi.gov/Departments/PoliceDepartment/tabid
Because it's more than real estate. It's RAYL-Estate!