Single public holidays have little impact on a travel in Japan.
Japan is one of the countries counting the highest number of legal holidays, to compensate the few payed vacations employees can actually take. Public holidays thus help working people to take a rest.
During legal holidays, public offices and companies are closed, but most of the museums, temples and other touristic areas remain open, as well as shops and restaurants.
If a public holiday falls on a Sunday, then the next Monday is considered a holiday. If a working day is included between two public holidays, it will become a holiday as well.
The only real difficult period is the Golden Week (late April / early May).