First of all, the graduate program director is definitely the person to talk to. There isn't much point in talking to the department chair; they don't necessarily have any direct involvement with the graduate program or admissions, beyond some nominal level of oversight. (Note that in some departments, the MS and PhD programs may have different directors, so make sure you get the right person.)
I think it's fine to ask to talk to the graduate program director. Graduate recruitment is typically part of their duties.
I would not necessarily expect that this conversation will directly improve your chances of admission. Graduate admission decisions are usually made by a committee of the department's professors, and at best the graduate director is only one of the votes on that committee. So no matter how good an impression you make on the director, the effect is limited.
Furthermore, the director will want to keep their decision based primarily on the objective information in your application file; it would be unfair if applicants who were able to visit the campus to meet them in person got a significant advantage over those who were unable to do so.
But it could be a subtle benefit. They might also have suggestions about things to emphasize in your application. And at a minimum, you can get more information about whether the program is likely to be right for you.
Email is usually the best way to get in touch.
Dear Professor Wu,
My name is Toby Ps. I am a student at the University of Wossamotta, and I am interested in applying to enter your department's MS program. I will be in your town between Octember 8-11, and I was wondering if I could meet with you or one of your colleagues to learn more about the program.
One question I have is about admission requirements. My overall GPA is X.XX, but I think this understates my preparation for graduate work because [reasons]. Can you tell me anything about how this affects my eligibility for admission to your program?
The second paragraph gives the director the opportunity to say "Sorry, we have a minimum GPA requirement of Y.YY, and we don't make any exceptions." If that's the case, it will save either of you wasting any more time.
Assuming that you are at least eligible to apply to the program, you can proceed to arrange the visit. If the graduate director is not available during those times, he/she may try to set up a meeting with another professor in the department who is knowledgeable about the program. You may also be offered the opportunity to tour the campus, sit in on classes, meet with current graduate students, etc; do as much of this as you can.
During your meeting, you can discuss the likely strength of your application. The program director (or other professor) won't be able to make any commitment about whether or not you would be accepted (admission decisions are usually made by a committee), but they may be able to tell you something about the qualifications that their successful applicants usually have, and that may give you a sense of your chances. They may also be able to give you their personal assessment of how strong your application would be; you can ask for this, but if they don't feel comfortable giving it, don't press them.
