OKUTAMA offers easy access by train from Tokyo city center and also it is a wonderful area of natural features.
For more information about Camping in Japan,THE JAPAN CAMP ASSOCIATION will be helpful.
Tel: (03) 3469-0217
They can probably advise on the best camping grounds for your family.
Also.....Nihon Auto Camp Kyokai (Japan Auto Camping Federation, JAC)
tel: (03) 3357-2851/fax: (03) 3357-2850. (URL:http://www.autocamp.or.jp/autocamp)