where the fallen radioactive dust goes?

I clean  and wipe my room.

where the wiped radioactive dust goes?

of course sewerage.

Tochigi prefecture (next to Fukushima prefecture) announced that incineration ash at sewer water recycling plants was found to be highly contaminated by radioactive cesium. it was 32,000Bq/kg.

http://www.pref.tochigi.lg.jp/h09/houdou/h230510odeir.html (japanese)

It makes sense very well. Radioactive cesium has been gathered and condensed at recycling facility.  It must be good thing rather than diffusing. 

Unfortunately one recycling plant in Fukushima found that  such an ash product was shipped already. When the contamination was found, sludge was 26,400 Bq/kg. Slag made from the sludge was 334,000 Bq/kg. Japanese government  announced to track the slag.

http://www.mlit.go.jp/common/000143547.pdf (japanese)