I would have said opium, until I started to do a bit of research after seeing you ask the question. According to Opium Regimes: China, Britain, and Japan: 1839 - 1952 (p 55), "...the almost total absence of drug abuse...under the old Tokugawa (or Edo) order..."

The authors then go on to talk about the closed borders policy and how that helped keep opium out of the country. There were also previous policies and treaties in place that forbade the importation of opium into Japan (p60).

According to Drugs and Narcotics in History, by Roy Porter and Mikulas Teich you could probably get tobacco by the time period we're talking about (p. 27), although it was illegal (p35).

Apparently they also smoked nutmeg for its hallucinogenic effects, but this journal won't let me log in using my university information, so I can't do much else.

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Why hasn't anyone mentioned alcohol? It seems to my unauthorised view to be the simplest, fastest way to get intoxicated by what is a very common drug. Cheers!

[EDIT] Amazingly, a search on "Hallucinogen Mushrooms in Ancient Japan does return something, although I'll left to qualified scholars of both said mushrooms and the 18th century Japan verify the validity on this one.