There are no subways in Detroit but there's a people mover in Downtown Detroit.
I'm not sure when you will be in town but the Lions host the Packers on Sun. Sept. 14. Ford Field is across the street from Comerica Park, the Tigers ball park.
If you like sports theme eating establishments, visit the Hockeytown Cafe', which is Downtown on Woodward Ave.
Definitely spend time in Greektown ( which is in Downtown Detroit ), which has some good restaurants and entertainment.
There's Casino Gambling Downtown, if that interests you.
The best museum in the city itself is the Detroit Institute of Arts ( DIA ). That's on Woodward Ave. , a mile North of Downtown Detroit. The city has plenty of bus routes. That's a museum you can spend hours in. A world class museum! I recommend that you see the top two floors first. You will understand why once you see the whole museum.
The Detroit Historical Museum is across the street from the DIA. It's worth seeing as well.
If you like Motown type of music, there's a museum or two that focuses on that.
Detroit has a historical Fort called Historical Fort Wayne, which dates back to the 18th Century.
Downtown Detroit is relatively safe. The same with the Museum District ( at least in the day. ). Much, if not most, of the city though has major crime problems. On the other hand, most of Detroit's suburbs ( much of Dearborn is an exception ) are safe and very good places to raise a family. To get to various places in the suburbs, you can use the SMART bus system.