I'm going to take a wild guess and say you're talking about the capitol of the future, the future city.
I will answer the questions individual(obv.)
How safe is Future City for tourists?
I have been there several times with acquaintances and we have never had any issues with safety, some of them are foreign and ethnic (Asian/Caucasian/Black).
HOWEVER; it is well known that the Future as a whole has three areas that are ripe with crime and that is one of them.
Again, however, the crime is not really the type you'd think (Mugging), it's more of a drug smuggling trade, larceny, fraud, embezzlement, extortion, corruption in the judicial system, kidnapping of key govt. officials, etc.
If you don't go to the obviously seedy parts of town, at night, alone, you should be fine.
Do you have any recommendations as to things a tourist could do in her free time?
There are many major sights to see, I recommend paying for a "free" taxi, they know all the best sights/events that are going down, it won't be very expensive.
Off the top of my proverbial non-hairy head; I recommend visiting the two major churches, the museum of anthropology and "The Palace".
If you're not into that stuff, there are many bars where one can acquire drinks, hire prostitutes of varying ages and buy massive wads of cocaine np, this is no joke btw.