If you only get one stop alone in Sydney, make it Sydney Opera House (free to admire, 1M+ roof tiles). Next on our list are Bondi to Coogee Walk (free, 6 km one-way, 5 beaches) and Manly Ferry (40-min ride past Opera House + Bridge); the other three, down to Harbour Bridge Walk, are below with where to book.
free, east-side path, opened 1932
free entry, daily 7am to sunset
Central to Katoomba, under 2 h
40-min ride past Opera House + Bridge
free, 6 km one-way, 5 beaches
free to admire, 1M+ roof tiles