Can I visit the Blue Mountains from Sydney without a car?

With just one day, I would focus on the Katoomba area and one or two lookouts rather than hop between several towns. The train gets you to the mountains, but the sights are not on the station platform; include the local bus or walking leg in your plan. If you want a long hike, sunset or a slow dinner, stay overnight. Trying to fit all three into a same-day return would be rushed.