Interesting problem. My observation/experience:
I think it is a very difficult place to comfortably move into an intimate space without either going somewhere designated for it, or ending up somewhere entirely inappropriate - and the places that fall into these categories are not as clear cut as we may wish for them to be.

I think it is very difficult to go to a love hotel and have an intimate night (of the sofa, TV ice cream, cuddle sort) partly because it's set out to be a place for other activities and there are channels on the TV that would make it very difficult to cuddle and watch! But as anxiety inducing as this might be it may prove more scarier for at least one of you to be going to the parents' house to have a cuddle and watch TV!

I think a lot of people find it very difficult to find a space to be really intimate in. So for the most part, as far as I have experienced and what everyone else seems to do, is to have their quiet conversations in their favourite local izakaya (which is very different, at least to a British idea of a local, in Japan it seems to provide a mental space that is an extension of your living room), and some of these "local" places are just outside of local so as not to be caught by curious neighbours (the Japanese seem to be very good at finding little private corners within two train stations away from their homes/work place. Other alternatives are cinema, Disney Land, and karaoke seems to be a good place to be naked (at least vocally) and where barriers start breaking down. I know a few of my colleagues go and stay in hotels in the city they work in with their partners to "get away" for a bit.

Just as an after thought (and sharp reminder from Mrs LapLap!) I found it easier to talk seriously about our relationship in the cafe Renoir. Ironically this is not a fabulous place by all means but it feels like a designated talking space and there are all sorts of different people there who come in to have a conversation, I seem to remember my meetings (not all amorous) to be either intimate or entirely unintimate - like a meeting with a distant aunt who you have no particular attachment to.