I'd recommend going on your own. Sydney is an easy city to explore by foot or by public transportation. Just plan an itinerary, grab a map and go.

You mention 3 things you want to see: Koalas, Opera House and Beach.

For the Koalas, you can take the ferry across the harbour to Taronga Park Zoo and see koalas and other native Australian animals. It's a lovely zoo with great views of the city. If you want an "up close and personal" experience with Australian animals, check out Featherdale Wildlife Park which can be reached by public transportation. See their website for details.

For the Opera House--you can't miss it! You can take a guided tour or you can attend a performance. If you go to the website and click on "What's On" and "Sydney Opera House on a Shoestring", you can find out about free and low-cost performances.

For the beach--Manly and Bondi are the most well-known beaches and are accessible by public transportation. A search of the Sydney TA forum will give you lots of info on the beaches and how to get there.

As for accomodations, I don't know your budget, but if you can manage A$135 - A$150, you can stay at either the Russell Hotel or the Sydney Harbour Bed and Breakfast (private room, shared bath). Both properties are located in The Rocks which is convenient to so many places you will want to see in Sydney. I have stayed in the Sydney Harbour B&B and thought it was great. The Russell Hotel gets great reviews too.

u can do the sights by yourself.

the explorer bus is a good start for orientation.

then just use public transport: ferry bus and train to get to the some of your destinations or simply walk.

there's the rocks, circular key and the opera house.

ferry to manly or bus to bondi (i prefer the former)

the zoo.

darling harbour.

china town.

the bridge...either the climb or the pylon or a simple wa;lk across.

centre point tower for a great view of the city and beyond.

queen victoria building for some shopping.

nsw art gallery, australian and powerhouse museums.

and dont forget the hyde park barracks on macquarie street. this museum gives u a great insight into the beginnings of european australia.

www.wotif.com.au for accommodation

and of course there is circular quay (u dont need a key to get there)

I also agree doing it yourself around Sydney and using a tour company/group for the Blue Mountains.

For Sydney, use the Sydney Explorer of the hop on/hop off open top deck bus around Sydney.

The ‘red’ Sydney Explorer bus visits 27 of Sydney’s most famous attractions such as the Opera House, Royal Botanic Gardens, Mrs Macquarie’s Chair, Kings Cross, The Rocks, Darling Harbour and a lot more.

It is the only timetabled hop-on hop-off sightseeing bus that stops north of the harbour and travels across the Sydney Harbour Bridge.

Each Sydney Explorer is air-conditioned and includes on-board commentary, giving you fascinating insights into the history and culture of Sydney.

This service can be picked up at any stop along the route. You can hop-on or off as you please, then simply catch the next bus when it arrives. Each bus operates at 20 minute intervals, allow two hours to complete the entire journey.

Tickets include unlimited travel on both the Sydney Explorer and the Bondi Explorer as well as regular Sydney Buses services in the Blue TravelPass zone. Tickets are valid until 4am on the following day.

Also try and include a ferry ride over to Manly. This can be done is an afternoon/morning.

have look at this recent post from a visitor who spent 2 days in sydney

tripadvisor.com/…12617442

Somewhere a bit closer than featherdale for an up close and personal experience with koala is Sydney Wildlife World next door to Sydney Aquarium. They also have quite a good reptile show... and they are a good slab cheaper than Taronga Zoo and quicker to visit as they don't have such a huge site and all the foreign animals. ...if you want to see platypus you need to go to the aquarium or Taronga.