It has been my experience that the most interesting places for rent in Detroit are never listed on the internet.

Find something acceptable that suits your budget and keep an eye open and an ear to the ground.

I suspect your definition of "bikeable distance" will shift when you've spent some time riding in the city. It's less about distance and more about having a good route.

And where ever you live, get some really good lights, keep them charged, and use them. People are getting hit all the damn time lately.