The lack of transit here in Detroit does suck. I'm going in reverse. Not having a car in Chicago is a feature, not having to deal with parking or traffic. If you stick to the central business district in Detroit, you can get away without a car & only stick to the pathetic light rail.
It'll get you to all the museums, sports stadiums, lots of other venues. But it's not super kid friendly. I admit I'm indulging in more train travel since my kid has grown - I have more money at this stage in my life & she's easier to travel with. (I travel more in general now, honestly.)