Did I mention, car-less?

I'll be visiting Detroit next week by myself, with boobs, feet, and a couple bucks in my pocket. Not much else. Can I get around downtown fairly safely without wheels, based on public transit, cabs, and walking? I'll be staying at the Inn on Ferry St, so there is a shuttle around downtown, but I also need to get to Dearborn and I'm wondering if the bus is a good idea.

Also... I'd love any suggestions for things to do or places to see next Sunday night or Monday during the day. Are there any areas between Ferry St/Woodward and the downtown core that I should avoid?

Thanks!