Sydney Australia, a few days

In Sydney I stayed at the Bondi Beach House located one block from Bondi Beach and a great jumping off point to walk the coast from Bondi to Bronte Beach. Lots of good food stops along the way. I ate breakfast at the Bogie Hole Café for salmon and eggs that was so good. No matter where you go in Sydney the coffee is freshly brewed.
Bondi has a saltwater pool if you’re into swimming laps. You’ll see helicopters circling over swimming areas to make sure the water is safe and I did see a fin that reminded me of a shark; that’s where the helicopter was hovering. You’ll need to take the bus to get around Sydney but it was easy.

If this is to be your first visit to Sydney then you really want to stay in The Rocks - the historic area where the city began. The area itself is beautiful with lots to explore in the immediate vicinity. It's just around the corner from the Opera House and the Botanical Gardens, and is a short stroll over to Circular Quay which is the transportation hub for the city - the ferries, trains and buses all depart from there, and are an easy and economical way to get around and explore the far flung reaches of the beautiful city, though our personal favorite mode of transport are the ferries which are an experience in their own right. Should mention that the the cruise ship terminal is right there a too. Pick up an Oyster card and just head out - you really can't go wrong no matter where you go. We consider it the most beautiful city on earth - it's our favorite travel destination,
Check out the "things to do" menu on TripAdvisor for an exhaustive listing of all the attractions in th city to see which ones most appeal to you, and I'd start with booking.com to look at accommodations.

It is a 2 hour train ride from Sydney to beautiful Katoomba in the Blue Mountains. From Katoomba station you could comfortably walk (or taxi) to a number of great features. If I was going to be in Sydney for a few days it would be on top of my list even though I have been to Katoomba many times.

We’ve stayed in a few different locations in Sydney. Most recently we stayed in Surry Hills and really enjoyed it. Lots of small cafes, bars, restaurants, old terrace houses. And easy to hop on the light rail to circular quay (tap on and off with your credit card).
We enjoy walking through the botanic gardens, maybe visit the art gallery and walk down to the harbour. Catching the ferry to Manly is a pretty nice way to see the harbour for a few dollars, although I guess you will be seeing the harbour as you sail out.
As mentioned, the Coogee to Bondi walk is very scenic (I found it a bit warm in January, but then I am a heat wimp).

Bondi Beach is nice and worth a visit, but some distance from Sydney. If you want to see the city, don't stay at Bondi.

Try to find a hotel near the Rocks/Opera house area. The Four Seasons is great and in a good location, but pricey.
We stayed at the Tank Stream Hotel, a smaller hotel, at a great location near the harbor. Rooms are a bit small, but adequate. Price is very reasonable.

There are a lot of great museums in Sydney, check them out. Also, do a harbor cruise and go to the Botanical Gardens. The zoo is great. Also, if you have time, take day trips to the wine country north of the city and the Blue Mountains.

The zoo was really fun. You take a ferry to get there, so it’s a great way to see the harbor. The zoo is on a cliff across from Sydney and the views are very scenic.

The Blue Mountains are just two hours away by train. The scenery is beautiful and there are many hiking trails, some quite hilly.