Katoomba is a sprawling town but most of the eating places and shops are within walking distance of the railway station. The sights, Echo Point etc. are at the opposite end of the town. There is a "Trolley" (a shuttle bus made to look like a tramcar) which operates during the day to get areound the sites.

Katoomba is actually on a plateau and the viewpoints look DOWN into the Mountains, a bit like Grand Canyon in USA. There are some interesting walks down in the rainforest.

The central tourist area of Katoomba is quite "tourist-y" (those who dislike this may prefer Leura).  There may be some gems hidden in amongst all the businesses catering to tourists, but the town council should work to change the current feel of the town.  The town itself is fairly hilly, if you go anywhere beyond the main tourist area.  It is possible to walk to the viewing areas like Three Sisters from the central business area, but wear comfortable shoes and you should be in fairly decent shape. (Distances are further than many of the tourist maps make it seem).  

You can also walk to Leura but be aware that the Prince Henry Cliff Walk is fairly rustic and rugged.  In most places, you can walk along Cliff Drive (no paved walking path but there is area alongside the road to get away from cars; this isn't a walk for peope with children). In the area around Leura Cascades, use Chelmsford Drive as Cliff Drive there has little room along the edges of the road, and is very winding so it's difficult for cars to see pedestrians.  Chelmsford Drive takes you through/into the Leura Cascades area.  The walk has a lot of hills, some fairly steep, so it's a fairly demanding walk.

If you're interested in the Prince Henry Cliff Walk, take seriously the need to be prepared with a good map, water, and other appropriate supplies like food and a compass.  In places it is well marked but the trail was not well marked in Leura. In many places, ferns grow across the path; it's easy to move through them, but some may dislike that.