Eyecity
In Japan you can't purchase prescription contacts without a doctor's visit. Eye exams are fairly simple and the prescription is usually valid for 6 months.
There are many places to buy contacts and lots of train stations seem to have a Eyecity nearby. (http://www.eyecity.jp/)
Non-prescription contacts are sold as beauty items and can be found in drugstores, make-up stores etc without a prescription.
mkawamura