From personal experience, I've done this a lot, having maybe done 12 interviews while working full time in 2013.
You can do an interview in 3 different ways without using a PTO day:
Beginning of the day (Starting your day by heading to the interview, then going to work)
This one is easy enough. Ask for the interview to be booked as early as possible. For work, say you have a personal matter and will be in later than expected. You can stay that same amount later, if you wish, to balance the hours.
During and as an extension of Lunch
This involves letting your supervisor know you will be running a few errands over lunch. Just leave for your lunch break, and cruise over to the interview location. This is much more effective if the interview is close.
After your day is complete
Booking your meeting for the end of the day is usually the best strategy if you don't want to miss a lot of work. Most interviewers will accomodate - and remember, CEOs and other entrepreneurs work very long hours. The majority I've known are still at work at 7pm.
Actually, it's amazing you have PTO days to even do interviews. Generally, as a contractor, you don't get paid a cent for interview time.
Also, it is completely reasonable to expect to do an interview after, or before, work. I've done many interviews around 5pm, 6pm, etc.
Potential workplaces are managed by professionals who understand you have important engagements with your time. At the point of scheduling the follow interview, all you have to say is, "That is great. I am very excited. I would need to come in sometime in the late afternoon, as I currently have obligations to my existing client."
About 95% of the time they will gladly accommodate you. The remaining 5%, what you are asking will actually not be possible, but they will probably have a number of other alternatives.
To close, you shouldn't jump too quickly at the chance for an interview. If an interviewer asks you to skip a day of work to come speak to them, and you do, what does that really say?
It says that you would do the same thing while employed by them.