It really depends on your budget and length of stay in Tokyo.
Sounds like a serviced apartment would be ideal. Google "serviced apartment tokyo" try Oakwood, Somerset, Duplex, Tokyu Stay to see what's available. It normally depends on occupancy whether or not a serviced apartment will be available for a short stay. For a few weeks stay serviced apartment is the only way to go.
People to people interaction as you suggest can be tough to arrange. For most Japanese, the language barrier is real and difficult to surmount. Kids in October are busy with school, sports and cramming.
Couple of suggestions -
JNTO runs a guide search database - perhaps you could find a hit there. www.guidesearch.jp/search/search.php…
Find out if the city you live in has a sister city in Japan and try to leverage that.
Shibuya Ward is planning "Peace-International City Day" in October. Perhaps they can arrange something??
International Cultural Exchange Section, International Relations Office, 1-1 Udagawa-cho, Shibuya-ku, Tokyo 150-8010, Phone 03-3463-1234 ext.2454 - 7