Circular Quay and The Rocks in sydney are quite nice - nice view and lots of food. Botanical gardens is also near by. Luna Park as well, although i dont think its worth the money they charge. Sydney aquarium and reptile park are right next to each other, although a bit pricey - close by is the imax theatre. The aquarium is freaking awesome though. I recommend doing it at night with the mrs for a more romantic atomsphere . There's also the maritime museum (darling harbour?) and natural history museum and art gallery (musuem train station). Is Fox studios still open? Never been there, no idea if its any good. If you wanna travel a little bit west of the CBD there is olympic park with some gardens and stuff out at Homebush Bay - perhaps worth a day. Go for a swim at the aquatic centre, ride a bike through the gardens or whatever they are called. If you really wanna travel, then the blue mountains are about 2 hoours west of the CBD. Go out to Katoomba (dress a bit warmer) and see the 3 sisters 'mountain' thingo and do some bush walking, zigzag railway (really steep train ride through the bush) and whatnot.
PS, all my american friends say that australia is pretty expensive, and sydney is more expensive than most. Be prepared to throw some cash around if you wanna do the touristy thing.
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