I grew up in the Detroit metro. The city was built around automobiles, and it's almost considered a sin to not drive places. You may also get shit for not having an American vehicle (regardless of where it was actually built). Public transit sucks. I'm sure that there are people biking, but realistically, you are going to need a car at least some of the time. Give it a try, but don't be surprised if it's really hard.
Geographically you are massively spread out here. There is a HUGE different between Auburn Hills and downtown. Do as much as you can to condense and live locally. You can't control work obviously, but you can control the rest of it. I'm not sure what the shaded areas represent, but the pins are a huge area. For example, I grew up on the east side of the bottom red area. Aside from work, people didn't go to the green areas.
You will also have quite the weather/climate transition. Right now, you've got sun and decent weather pretty much year around. Detroit is not the same. It is very possible to not see the sun for 6+ months in the winter. Be prepared for that shock.
I don't know what ethnicity you are, but that is unfortunately a real issue. Black, white, yellow or polka dot, you will run into problems SOMEWHERE in there. A lot of Detroit's problems are rooted in racism, and it shows.
Detroit has been getting better. Their school system is possibly the worst in the country. A large part of the population is poor and poorly educated. A large chunk of the former population has left. The city has issues with corruption. (Yes, it actually is better now than it used to be, but when it starts out as bad as it was, it's not easy to fix.)
Practically speaking - pick the main blue spot. Locate near it, but be cognizant of access to major roads and needed things like grocery stores, etc. Rent for a year, and figure out where you actually want to live. Then move to that area.