Wake up nice and early today to catch a train to the Blue Mountains. They lie 3 hours away from Sydney. The Blue mountains line runs from Central station to the mountains, but you can buy tickets anywhere in the central loop. Buy yourself a lunch at the station, as there are not many places for a sit down lunch, mainly if you want to see & hike a lot.
Get off at Katoomba. Right outside the train station is the Explorer bus booth. Buy tickets to the scenic world and the bus tour. Here's a tour map.
Finish the scenic world attractions first. It takes 2-3 hours depending on how much of the Scenic walkway you decide to take. 40 minutes was good for us, but you can choose here. Eat your picnic lunch here as well.
Ride the bus now to the Echo point for beautiful views of the Three sisters. After a half hour here, you can head to either Leura cascades or Gordon falls for a quick hike (or bushwalk as they are known locally).
Now head to Leura village. Get off at stop 21 and make a right to a bright yellow teahouse called "Bygone Beautys". They usually have a two for one Devonshire tea coupon in your booklet. Use it and enjoy a heavenly English tea complete with amazing scones, jam & cream.
Head back to Sydney to enjoy some great dinner and the amazing nightlife the city has to offer.
http://www.theargylerocks.com/ is a great bar to visit.