This review is specifically about crossing the Sydney Harbour Bridge (free) - this does not review the climbing tour experience ($$$!).
I have crossed the Sydney Harbour Bridge several times as part of various running paths around Sydney. Accessing the pedestrian bridge is a bit tricky from the Rocks area - one can follow the bike path uphill to find the covered stairs. Once taking the stairs, note that the entrance is not at the top of the stairs, it is one level before the top.
The walk is easy and does provide a fantastic photo opportunity of an "aerial" view of Sydney Harbour and the Opera House. Note, one would have to take shots between the protective fence links. There is a pylon about halfway across the bridge which one can climb to obtain additional views. The path is safe and there is always a guard at the pylon view.
Because the bridge also provides access to cars, I do not enjoy the experience as much because of the fumes/exhaust. This is worth one visit for the photo opportunity, but there are several other Sydney sites to visit that are more enjoyable.
This review is the subjective opinion of a TripAdvisor member and not of TripAdvisor LLC.