I go jogging some nights. I do it at like 2:30 AM because I'm fat and when I take my shirt off, I don't have to worry about blinding anyone because hardly anyone is out during that time; although sometimes I feel like the drug dealers are laughing at me, so I always put my shirt back on when running by the heroin dealers.
South of the Gateway mall there's a ton of homeless people along with TONS and TONS of drug dealers/users. It probably wasn't the best idea to build a mall directly next door to a homeless shelter. Pioneer park is about 100 yards away from the mall and is where the homeless hang out during the day time. Anything immediately West of the mall is going to be homelessness, drug dealers, and prostitutes. In the winter, the homeless will travel East to the Library to stay warm during the day, but they rarely travel East in warmer months. All the night clubs are located deep within this shit; so if your daughter is a club goer, she might end up in this area. That small quarter to half square mile area is probably the ugliest part in the entire state. My typical jogging route takes me right through the shit and despite the run down appearance and all the bad elements around, I would still say it's a lot safer than other parts of the country. I never carry when going through that part of town, never had a problem with anyone there, and never seen anyone engaged in any trouble they weren't directly responsible for. My wife is 5'4 and 105 pounds; she frequently walks through the shit area to catch the train and she's never had an issue with anyone except for one lady who tried to steal her laptop on the train. She has a conceal permit, but never carries because she's a Federal employee and firearms aren't allowed in her building.
Outside of that little tiny area, the rest of the city is really safe and shouldn't be a problem for anyone, male or female, regardless of age. Downtown is pretty busy from 6AM until 8PM, but then as if someone were flipping a light switch, the entire population of the downtown area seemingly disappears with the exception of the shit area near the homeless shelter which always seems to have the same 400 people slumming around.
I've drawn you a map of the shit area in case you were wondering, it's outlined in red. Don't worry about the other colors on this map, I drew this up for someone else.