I've seen quite a few shows that were really up close and personal with the actors, including most of the events at the Campbell House Museum, and Wolf Manor's Richard III left the audience really close to the action. I saw Lear really close up as well in Vancouver (I believe the company was the Honest Fishmongers). In most of these cases, you have two rows of seats around the stage, and if you choose you can be in the second row (generally a good decision if there will be swordplay or blood gushing as in so many of Shakespeare's historical plays).
For Conor McPherson's Port Authority, they turned the downstairs room into a pub (with a working bar no less), and you could sit at any table you chose. If you showed up early that is. We made it inside by about 7:15 and most of the tables had been taken, though we could have had seats with our backs to the performers, which then means turning the seat around and is generally a bit awkward. That left the two tables up front, right next to the three chairs where the performers would be. I would say we were within 5 feet of the performers and they often looked right at us, though only occasionally talking directly to us. This was definitely a bit of a different play where the focus was on characters who by their own admission kind of let things happen to them, i.e. they weren't doers for the most part. That is a bit different from many plays, particularly American plays, though sometimes you have a character like Willy Loman realize that he no longer is a mover and shaker and that realization is the tragedy -- for an American audience especially. Two of the three characters seemed more content with their lot, at least in terms of their occupations, but then they still had unrealized longings for something (or someone) that just seemed out of reach.
I would actually recommend one table back from where we were (where you thought if you reached out you would touch the actors), but there is no question that this is an intimate evening anywhere in the room. It also means that there are not a lot of seats at each performance. I would be surprised if they have more than 36 spaces per show. Nonetheless, the actors did ask us to spread the word, so if you are interested, you should check here to see if there are any further slots open for the last week of performance.
I don't really know why this is called Port Authority, aside from Dublin actually having a port, and at one point one character discusses taking a long walk down to where you could see the sea stretching out endlessly.