As Silouan stated, you will need to obtain a pass to visit the Holy Mountain. I believe a letter from your priest introducing you as an Orthodox Christian in good standing as well as a copy of your baptismal certificate would be helpful in obtaining this. I just returned from there, but I can't give you much more information than that because all my paperwork was taken care of by the gentleman I traveled with, a fellow who had been to Athos over 100 times and was well-known in most of the monasteries and sketes there.
While it is certainly possible to tour Athos alone--while there I met a young solo pilgrim from Pheonix Arizona--your trip will be much more rewarding if you can go with someone who has been there a few times and is known to the monks. Relationships count for a GREAT deal on Athos, and throughout Greece for that matter. Having at least one Greek-speaking member in your group helps a lot too.
However you get there, you will love it once you do. Athos moves you in ways that can hardly be expressed. Don't forget to ask the intercessions of the Panagia, or our Most Holy Lady Theotokos, as part of your preparations. According to tradition, she is the Protectress of Mt. Athos and no one can set foot on the Holy Mountain unless she grants it and opens the way. Knowing that makes arriving there all that much more of a special experience, and you can expect to grow in your appreciation for her all the more as you witness the many miracles she has wrought for her beloved monks.
God bless your journey!