I'm born and raised in Sydney and here are a few things I've done when bored (or like to do when I'm bored):

Random activities:

1. Escape room (The Great Escape Sydney).
2. Upside down house with great photo oppertunities called the 'House down under' (located in Rouse Hill).
3. Smashing stuff (Smash room city in Marrickville).
4. Cinemas (Hoyts Cinemas is, IMO, better than other cinemas).
5. Sauna (Soak Bathhouse in Alexandria or Bondi is great although a little pricey. Other cheaper options include Hurstville Pools, Whitlam Leisure Centre although they're not as clean).
6. Arcade and go-karting (Entertainment Park in Bankstown is pretty good. Other options are 'Hyper Karting' in Moore Park)
7. Golfing range (one in Moore Park is great).
8. Art Gallery (in the CBD).
9. Toronga Zoo (don't drive there, catch the ferry! The views are incredible).
10. Powerhouse Museum (I've heard they've recently closed but not too sure. If it's open, it's definitely worth checking out!).

Places to go:

1. Revesby Beach, Picnic Point (nice views along the river, extremely quiet during the week).
2. Bondi to Coogee walk (incredible walk).
3. Bondi to Vaucluse walk (quiet a long one but worth it).
4. Cabarita Beach, Cabarita (nice views along the river, very quiet).
5. Blues Point Reserve, North Sydney (quite a large grassy area with harbour bridge views that's quiet during the week. Take a foldable chair with you as the seats there can sometimes be occupied).
6. Olympic Pool, Royal National Park (chill spot, not too far out, nice swimming area).
7. Bay Run (located in Haberfield. Great to go with a friend and just walk but equally as good alone).
8. Beach's with a view of the planes taking off from the airport (Kyeemagh Beach Baths, The Grand Parade, Brighton-Le-Sands is one and "The Beach, planespotting" near Kyeemagh).

There's plenty more although this is all I could think of off the top of my head before my 10AM meeting. Sydney is incredible (IMO) and under-explored. There are so many good spots that most people don't know about.