Should I quit my job and travel the world before applying to PhD programs?
The way PhD admission works is that you usually apply during the fall, receive admission decisions in the following winter/spring, make a decision around April and enroll in the fall. This means that there is usually a four-month(ish) long gap between the admission process and enrollment. Many students fresh out of college will use this period to relax, maybe even travel around the world. So if you can afford to quit your job or make certain arrangement with your employer, this time window could be a compromise between your need to enjoy life and appear productive, since people don't usually expect you to work hard just before you formally enroll in the program. On the other hand, if you urgently need to travel well before application and still want to impress the admission committee, my general advice is that a generic travel plan will not achieve the goal here. For your travelling to be viewed positively, it should yield concrete outcomes demonstrating excellence in whatever skills valued in your field of study.

I should also say that this is based on my experience with Ph.D. programs in science. A political science Ph.D. may have difference culture/expectations.