There are two kinds of conversations that are great. The first kind happens when you want it to happen. By this I mean, you choose to talk to someone you expect to have a great conversation with and you set up a context where conversation is likely. Sometimes this means sitting someplace quiet; sometimes it means attending an event and following up with an opportunity to talk; sometimes it means going for a walk or a drive. In all of these situations, you are intentional about who is part of the conversation and where it happens.
There's another kind of great conversation. It's the kind you don't intend and don't expect. These conversations happen in rich environments where people are in that interesting state of being enlivened by their work (whether or not it's paid work) and temporarily detached from it (maybe they've stepped out for a bio break or maybe they are doing an errand, for instance). Lots of research shows that creativity happens when lots of different people are in an environment that encourages random interaction.
I remember university this way. In one respect, we had great conversations because we were set apart in classrooms or residences. In another, we came from very different backgrounds and interests and we had conversations mostly because we had all ended up in the same place at the same time and we all had lots of energy and openness (because we were all 19). Sometimes, we even had amazing conversations with our professors (but not usually while we were in class). Even in a setting where great conversation was an expectation (I attended class in small seminar groups where everyone was encouraged to participate), the best conversations were the ones that just happened.
It's a paradox that science says that this kind of unscientific, unprogrammed conversation is exactly what we need to produce great ideas. It's a paradox that a business which really values productivity must adapt to make time for what are superficially unproductive moments of random interaction.
It's not a paradox in the arts. In the arts, the best lived life wins. And the best lived life has always had room for great conversation in unexpected places.