I arrived in Katoomba on Christmas Eve and had opted to stay at a backpacker's hostel in order to meet some like-minded others and be on the outskirts of the Blue Mountains National Park. The walk to the park entrance (and Three Sisters viewing point) was less than 3km and took around 40 minutes. The walk was along mostly flat road and had signs pointing to the Echo Point lookout. Once there, you can take the cable car to the Scenic World for more astonishing views or opt to take one of the hikes to various places, including the Scenic World or neighbouring towns; Leura, Wentworth Falls and Bullaburra to name a few. I did two major walks over the course of three days, including enjoying a ride on the world's steepest railway. A one-way ticket will cost $19 if you've managed to hike to the bottom and aren't so keen on trekking back up to the top. Alternatively, take a ride on the Blue Mountains Skyway - the cable car with a glass floor offering 360 degree views of the surrounding mountains, definitely not for the faint-hearted. A ride on the Skyway also costs $19 for a single adult.
Katoomba is very well-priced regarding food, beers and accommodation. There are plenty of activities to do which range from free hikes to organised canyoning and caving trips. If you like the outdoors, other surrounding towns offer camping experiences and in the winter there are plenty of places providing log fires and hot tubs for those who like to cosy up.