If you have never spent much time in the Detroit area, whether you are looking in the city or a suburb or are not sure which you want, I recommend renting a place before seriously considering buying. There are a lot of rental houses available if you want to live in a house. Once you are in the area, you will be able to get a much better idea of what towns/neighborhoods are appealing and affordable. You will probably get a lot of questionable information from people even after you arrive, but you will be in a better position to evaluate it. I would be even more emphatic about this if you are planning to live inside the city limits, because what neighborhood or even block you live in can make a big difference in your quality of life, and you are not going to know enough to make that decision until you have been around a bit.

Given that you still have school-age children, you should probably give the availability of schools some consideration. The quality of the schools varies widely from town to town, as it does most places in the US. Most people with an alternative would not choose to send their children to the Detroit Public Schools, although again they are not all equally terrible. There are other options for people living in the city, but they are often more expensive or less convenient or both.

Good luck!