There are a number of walks you can take in the mountains to experience them, where the tracks are well marked and well traversed. You can walk from Echo Point to the Scenic Railway, down the steps at the Three Sisters, and take the Scenic Railway back to the top. These walks have mobile reception, and you will have no problem following the tracks. There are shorter walks at Echo Point too. Check at visitor information.
If you are bushwalking any further, you should prepare for the possibility of getting lost in the bush. People get lost regularly, it gets cold overnight, and visitors and mountain locals have died when they have lost the trail, and become disoriented. Personal locator beacons are available free of charge from Katoomba Police (http://www.police.nsw.gov...). Let someone know your route, and when you will be back. Take a mobile phone not always in range and a GPS.