I have tried to list the activities below in the order that you can walk them. The greater CBD can probably be done in 2 days.
Royal Botanic Gardens http://www.rbgsyd.nsw.gov.au/
The gardens are a real jewel in Sydney’s crown and you could easily spend an hour or two wandering about and enjoying the views or relax in a shady spot.
To get there, catch a bus from across the road on Bayswater Rd to Circular Quay (just ask the driver).
Another option is take a most enjoyable walk from Potts Point. Turn left out of the Holiday Inn and walk all the way down Victoria St and turn left down a long set of steps (McElhone Stairs) that will take you to Woolloomooloo Bay and the Naval base. Cross the road and walk past the Finger Wharf Apartments (pie cart on your left) and turn right at the marina and proceed along the boardwalk as far as you can. Take the set of stairs on your left (they are obscured by the stone wall so look carefully for them) going up to the domain and the edge of the gardens. You can walk around Woolloomooloo Bay to Mrs Macquaries Point and views of the harbor and cityscape before entering the gardens.
Note: This is also the route to Boy Charlton swimming pool (refer to swimming section)
Opera House http://www.sydneyoperahouse.com/
You can either go on a tour or simply walk around the Opera House and marvel at its uniqueness and beauty.
Circular Quay http://www.sydney.com.au/quay.htm
Circular Quay (next door to the Opera House) is full of activity. It is a major transport hub for ferries, trains and buses. There are often buskers to watch and entertain you.
The Rocks http://www.therocks.com/
The Rocks is the oldest settlement in Sydney and is well worth a walk up and down its narrow alleyways.
You get to The Rocks from Circular Quay.
Find Argyle St and at the lower end, just around the corner from George St is a pastry shop called La Renaissance, and their pastries are awesome, especially their almond croissants. http://www.larenaissance.com.au/index.html
Each weekend, The Rocks markets operate and they are well worth a visit to check out all the stalls. Several streets are closed off and it is a carnival atmosphere.
All of the above activities could be combined in a day. If you do not feel like walking back to Holiday Inn, get a bus, using your mymulti, back from Circular Quay. Click on the link below to find the bus number you need. There are lots of options (324, 325, 326, 311 327) as loads of buses go through Kings Cross.
An awesome way of viewing Sydney is from the water. The ferries transport locals from many of its waterside suburbs and you can hop on a ferry and do a round trip, or get on and off as much as you like. Remember, your mymulti works for the ferries to.
Short ferry rides are an excellent filler if you want to just take some time-out and sit and relax.
Ferry trips I recommend:
Mosman (approx. 30 minutes return)
Neutral Bay (approx. 20 minutes return)
Darling Harbour (approx. 40 minutes return)
Manly (don’t take this ferry yet as more on Manly later)
Check out ferry departure times on the monitors at each of the Circular Quay wharves (also informs you which wharf your ferry departs from).
Another day in the CBD
This is the city’s central open green space. It is a beautiful place to walk through and a very popular spot for office workers to take some time out from the city. 30 minutes should be time to walk around the park.
To get there from Potts Point, when leaving Holiday Inn turn right and walk to Williams St (large Coca Cola sign on your left). Turn right down Williams St and keep walking for about 15 minutes and you will have Hyde Park on your left and right. Check out both sides.
Pitt St Mall
A block west of Pitt St, located on the corner of George and Market Streets is the Queen Victoria Building and it is noted for its architecture. Check it out. Time for a coffee? Across the road on George St is Espresso Workshop (nearer the southern entrance of QVB).
You can walk over this iconic landmark. The walk is quite breathtaking and takes about 30 to 40 minutes to cross, including stopping to look at the views.
To get to the bridge from Potts Point, I find the easiest way is to get the train from Kings Cross to Martin Place Station which is the next stop from Kings Cross. You need to walk to the Rocks and look for the bridge stairs on Cumberland St. These stairs take you up to the pedestrian walkway for the bridge. If you get lost, just ask a local.
On the other side of the bridge you will enter the suburb of Kirribilli. Check out the village and it has some nice cafes.
To get back to the Holiday Inn you have 3 options.
Option 1: take the train (get to train station about 100 meters from bridge stairs you came down) to Central and change to platform 24 for Eastern Suburbs (Kings Cross).
Option 2: walk back over the bridge and catch a bus from Circular Quay,
Option 3: catch a ferry from Milsons Point back to Circular Quay and catch a bus. To get to Milsons Point ferry, walk down the hill at Kirribilli and follow the walkway (under bridge) and you will see the ferry wharf opposite North Sydney outdoor pool. Catch a bus from Circular Quay.