You could do a lot worse than the Captain Cook Hop-On, Hop-Off Cruise. The ferries are all wheelchair-accessible and there's some basic guide-style commentary as well.
The list price for the all-you-can-ride 24 hour pass is also $40 per head, but they've got good deals with many attractions so you can get, for example, the pass and Sydney Tower or Sea Life Aquarium for $55 combined, vs. something like $80 separately. Cheaper yet, you can buy a return ticket for a suitably distant attraction (say, Manly at $18) and then pick a service that happens to visit all the points you want to see -- they're the same boats! Alternatively, you can pay a bit or a lot more and get meals, entertainment etc on board with Captain Cook or any of a number of competitors, although (IMHO) these are not great value.
The even-cheaper alternative is to just use regular public transport Sydney Ferries to explore. With an Opal card the fare caps out at $15/day, your elderly companion may qualify for the $2.50/day cap, and everybody can ride all they want for $2.50 on Sundays. These, too, are all wheelchair-friendly.