Both births were in the local maternity hospital. There was not really a question as to whether I would be present, it was assumed from both sides. My wife went to NCT classes where this was very much the assumption and I went along to the ones that were specifically intended for Mums and Dads. The preparation was good so that I (and we) knew what to expect, and when it was clear the birth was about to happen, we went to the hospital and it happened very much as expected. We were fortunate that there were no real problems, indeed for the second birth we were back home within 12 hours of leaving (it was Christmas eve and they were keen to get everyone home for Christmas). From what I remember the hospital was very laid back and were happy for me to be there, or not be there for the birth. We were left alone as just the two of us for a reasonable amount of time in the hour or so before the birth, which I hope/expect would not have happened if my wife had been on her own.
We had not been to the maternity hospital before the first birth. I gather from facebook comments that an introductory visit to the maternity unit prior to the birth is fairly standard.
There had been so much preparation for the first birth that immediately afterwards we were left with a sense of being relatively unprepared for what happens next.