Close to

sights near the house,

adventures:

that will make your head spin!
The Blue Mountains is an absolute must if your in Sydney. My recommendation is purchasing an Opal travel card which for those in the UK is the equivalent to an Oyster card. Catch a train from Sydney Central to Katoomba. From Katoomba, go to the Hop on/Hop off bus tour shop and purchase the $89 package which allows you to use the bus and all 4 of the scenic world transportations. It's truly the most beautiful place I have ever been. If your hikers there are plenty of hikes, if you just want to wonder around there is plenty of that too.