Haven't done much of the "dating" thing in many years, but back in my 20s, my average Friday night with the other half generally began at an izakaya with alcohol, then a darts bar with more alcohol, and ended up with us staggering down the shotengai, taking drunken lewd photos and then sloppily trying to fuck in the purikura booth (and I always left the curtain a little open so the high school kids could see what was going on).
But a mature, daytime date? I don't know. A nice lunch somewhere? A museum? Someone mentioned Ueno Park...do they still have those corny rental boats? If she's kinky enough, maybe you could get her to fuck you on the water while all the other couples and families watched. You'll definitely end up on Youtube.