There is a native botannical gardens at Mt Annan. They cover a large area which was once pastural. Definitely worth a vist for the native plants and gardens. It is just off the Hume Highway (M5) between Camden and Campbelltown. Other than that, there is the botannical gardens in the city, and there are many open gardens in the Blue Mountains. Hope this helps.

Also try the Botanical gardens at Mt Tomah in the Blue Mountains

How about Royal Botanical Gardens, in Sydney, always a lovley spot.

Then there is the Chinese Gardens at Darling Harbour, you have to pay to go in there, but I dont think it is a lot of money.

Even the Zoo has lovely gardens.

Lovely weather for looking at lovely gardens.

Popi

kkaren the botanic gardens in sydney has a huge glass house that has been crammed with rainforest/tropical plants, but i think there is a small fee to enter, but well worth it, Mt annan botanic gardens is a fair hike from sydney and they have a small rainforests section scatteded throughout if but last time i was there it was slightly disapointing, Mt tomah is even further but well worth the trip as it is set in a lovely location. If she likes Grevilleas theres a great garden in wollongong well worth the visit .....and the soath coast is always lovely....

try checking out the Open Gardens scheme. They have some details on the website, from the highlights on there at the moment it looks like January is a bit of a down period for them, but you can ring 1902 261 026 to check if you're keen.
If heading up the mountains, there's usually a range of open gardens, best to check with the local info centre when you're there.

The zoo is indeed well known for nice gardens, but I'm told it's something of a construction site at the moment, and with such a hefty entrance fee my informants weren't impressed (even though they're manic zoo visitors)

If by some chance your friend decides to check out Canberra (only about 3 hours or so by car from the heart of Sydney these days), there's gardens there worth seeing.