Korea is 1 year without your family, two years with, and Japan I believe is 3 years with no family restrictions. You can usually extend an extra year in Korea if you want and so far only 1 dentist I know of has deployed from Asia and that was a few years ago. You never can tell what the future holds though.
If that is your main concern, I would recommend playing hardball with your recruiter and telling them you won't sign the contract unless you can be guaranteed Korea or Japan as your first assignment (go for Japan first, if they say no, try for Korea). The recruiter will have to contact the "branch manager" in charge of dentists assignments to get an answer for you, don't let him say you'll have no problem getting your choice, instead make sure you get it in writing from the branch manager. They do this all the time for soldiers reenlisting or for dentists coming on active duty, so it is not really out of the ordinary, just usually HPSP applicants don't know enough to ask about it. Truthfully, you shouldn't have any problem getting Korea, but better safe than sorry.
Good luck.