Katoomba and the nearby Leura are both relatively small towns, it can still take tens of minutes to walk between the various attractions. You can choose to hop on the Blue Mountains Explorer Bus (more frequent but more expensive) or the Trolley Shuttle (cheaper, less frequent, last bus runs later) to get to various attractions faster, and save your time for good hikes along the cliff or the valley.
Scenic World is a major attraction in Katoomba, claiming to have the steepest railway in the world (Scenic Railway), the highest cable car in Australia (Scenic Skyway), the biggest cable car in Australia (Scenic Cableway), and the longest boardwalk in the Southern Hemisphere (Scenic Walkway). Scenic World takes a good 30 minute walk from the Katoomba station, so you'd want to take the Explorer Bus and get off either at "Skyway Eastern Anchorage" (the east point of Scenic Skyway) or Scenic World.
The Scenic Railway apparently holds the Guinness Book of Records for the world's steepest railway. The official certificate says it's 310m long with a gradient of 1 in 0.82, while the sign post in the valley claims it's 415m long with a 206m vertical drop, a 80m long natural tunnel, and with a steepest incline of 52 degrees. Anyway, it's definitely a worthwhile ride, especially if you can get in the front seat like I did!
most weather conditions.
I chose to take the Cableway to go back up. It's a huge cable car that claims to be able to hold 84 people. And I also took the Skyway that has a good view of the Kaboomta Falls, and has a part of its floor transparent to see the 270m drop.
Echo Point is a great place to see the Three Sisters and blue mountains at a distance. Below are some of the pictures my colleagues and I took. You can visit my album at Google+, which offers a great photo viewing experience.
There are several nice hiking trails in the vicinity. I took the cliff walk that has several great outlooks. Although the weather is good at the time, some parts of the walk are muddy from the continuous raining previously. On the bright side, waterfalls are likely to be more spectacular. Below are shots of the Leura Falls that is highly recommended by the bus driver (we were originally planning to check out Gordon Falls but the driver persuaded us otherwise).
A colleague has suggested us to go to Leura for great restaurants after visiting Three Sisters and Scenic Railway, so we pulled out Google Maps and found Silk's Brasserie which had a 5-star rating. Below are photos of the Pan-seared scallops with avocado, salmon, tatsoi salad, light wasabi dressing and the Roast Moroccan lamb loin with couscous, pine-nuts, date, tomato relish + spicy harissa dishes that I ordered. They are indeed very good!