Well not sure what you mean by cheapest area to live in Hong Kong, relative to size is what matters. If you are looking for like 100sq. feet or something the best deals will be out in East Kowloon and maybe even Sham Shui Po/Cheung Sha Wan area.
If you are looking for a proper flat type deal 700sq feet or so than maybe heading for like Sai Kung and Clear Water Bay may be suitable. Get half of a village house for $6000-$7000 often times.
Depends all the features you want.