Okay, I think this has gone on long enough. You're all on the right path, but I don't think you're going to get there.

The key word in the original question was "segment" rather than "flight". I am, indeed, referring to SFO Helicopter Airlines and they did fly the S-61 (S-58 before that). What I was looking for, though, is the couple hundred yards between gates 55 and 44 at SFO. Most, not all but most, of their flights served both gates, and the helicopter would just taxi from 55 to 44 (I don't recall that it ever went in the other direction).

I don't have the timetable here at the office, but I think the flights to PAO and SJC were exclusively gate 55, and some to OAK were one or the other but not both. Most flights, though, show an arrival at gate 55 followed by an arrival at gate 44, or a departure from gate 55 and then a departure from gate 44. A lot of these, of course, overlapped: flight XXX coming in and flight YYY going out, but the same times at the two gates.

I remember standing on the observation deck and watching them just taxi from the one to the other before taking off from the taxiway. I never had the opportunity to take a flight, since we lived on the Peninsula just a few miles south of the airport, but I always wanted to.

The timetable varied over the years, of course, but typical routes were:

Not that I'm aware of. I think the downtown Oakland location changed at some point, but before I was old enough to really be paying attention -- or it could have been just the name of the building changing.

In a bit of coincidental irony, when I was at Barnes & Noble the other day picking up gift cards for Christmas I wandered over to the magazine rack and picked up the October issue of Airways. The first thing I noticed on the cover was an article on the helicopter airlines of the US! This was part 1, though, and SFO must be in part 2. This article does cover Los Angeles, Chicago, and New York.