Certainly, there is crime in the area, as West Philadelphia is within walking distance. But frankly, between Drexel and the University of Pennsylvania, there is plenty of security to go around. Throughout University City, you will see Drexel security officers, Philadelphia police, University of Pennsylvania police, and emergency posts—don't forget the bike cops. It should also be noted that if a student is ever frightened of walking alone, a free escort service can be utilized by calling Drexel security. Also, the Drexel shuttle travels between Center City and Main Campus until 11 p.m., which is super convenient for students if they prefer to not take SEPTA at night. Of course, a certain degree of "street smarts" is recommended. Realistically, you'll be fine if you stay away from unfamiliar areas, avoid traveling alone (especially at night), and don't draw unnecessary attention to yourself.
While security is of the utmost importance, health is right up there next to it. Most students will agree that the Student Health Center is more than satisfactory. A wide variety of services is offered to students, mostly due to the high population of international students. That being said, the hours of the clinic vary by day, so it's wildly important to check beforehand, as it opens and closes throughout the day. In addition, they've added an appointment-based system versus simply walking in. They're usually quite accommodating—just be sure to call ahead.