Besides just walking around and getting a feel for the city (which is a must wherever you go) there are a few activities that I was really happy I got a chance to do.
We took a day trip to the Blue Mountains. You can go on your own but we took a tour with Boutique Tours. I'm glad we did that. I think we learned a lot more having an experienced guide. Plus we saw all the best things. If you like nature, hiking (but not serious hiking), bird watching (Boyfriend's favorite), sweeping views, and just being outside you'll like it.
I loved the Taronga Zoo. You can walk around with Kangaroos! Boyfriend was happy because he got to see a platypus. It seemed like it would be easy for some animals to escape. They weren't as caged in as other zoos I've been to. I guess that made for a better viewing experience. I was chased by an emu which was traumatic but getting to see all the cute, lazy, fat koalas made up for that.
We went to the Hunter Valley which is 2 hours outside of Sydney to go wine tasting. I think it's hard to not have fun drinking wine all day. I mean, I bet tastings in France would be way better but whatever. I'll save that for another trip. Boyfriend is more of a wine snob than I am but he ended up having fun too.