I was thinking that the character would be a moderately active teenage girl that's 5"8 and 160 lbs. The speed itself is a super-power and she is otherwise a normal human. I'm defining safe as a speed that wouldn't kill or seriously injure her.
There are two ways we can look at 'safe' speeds for your teenager;
1) How fast can she run and an unanticipated collision not kill her, and
2) How fast can she run without her body breaking.
Dealing with the impacts of collision first, the answer is not all that much faster than a normal human can run. If you look at Olympic sprinters for example, they run as fast as they can to get to the line, but they don't come to a dead stop afterwards. They have to slow their momentum down gradually. The race would look very different if (for example) the finish line was in fact a finish wall and the first person to touch it won. People would have to slow down at least a little because at a little over 25 Km/h the damage that running into a brick wall would do to the body would be substantial, especially depending on what part of you hit first. You could blow out a knee, damage your knuckles to the point that you put your hand out of action for at least a temporary period of recovery, and potentially even knock yourself out if you hit your head the right (wrong) way. So, at any speed faster than that, the momentum increases meaning that the damage that can be done by a collision also increases.
As for her body, there are a number of ways that being able to run that fast could go wrong. If her muscles are capable of super fast twitch actions, they could move so quickly that they could literally tear themselves away from the skeleton by ripping the tendon or other ligaments. They could tear themselves apart, or even snap bones like the Femur depending on things like bone density and muscle development. Even if all that wasn't the case, like a cheetah you're only going to have a small window of super speed because you simply cannot get the energy requirements to the muscles via the bloodstream fast enough for sustained super speed. Just like Cheetahs, you end up overheating with that short physical exertion as well, limiting the time you can run to a given period after your previous one for cool-down. Put simply, running too fast or for too long will kill you; just look at how the Marathon got it's distance and name.
The Cheetah is in point of fact at the upper end of a biological niche for running at speed and most studies on the animals show that they could not run faster without significant sacrifices to their biology that are potentially non-viable. As such, we could say that the Cheetah's top speed is a biological limit for your teenager, but in reality it tops out much sooner because humans are simply not designed with the tendon & bone strength, and the fast twitch muscle design, and the blood supply system, to take advantage of similar speeds.
Evolution tends to favour efficiency over any other factor, so as a result our skeletons, blood supplies, muscle design, tendon strength et al are designed to support the upper limit of the average human's performance as a general rule. This means that unless you make other changes, the top 'safe' speed of your teenaged flash is actually pretty close to modern sprinters, or around 25 Km/h. The higher you go after that, the less safe it becomes and ultimately your top speed is REALLY set by the amount of risk you're willing to take. After all, even Olympic sprinters choose when they apply that kind of speed and don't run everywhere recklessly.