The cheapest and easiest way to get from Sydney to The Blue Mountains

Costing only $2.50 return for a Senior (over 60) this is unbeatable value. For standard adult fares it's still a great deal (single tickets are around $10.00, Opal Card fare $8.50, 30% less if you travel Off Peak. Travel all day on Sunday for only $2.60 (trains, buses, ferries).
Central Station, Sydney to Katoomba is a 2 hour trip with limited station stops. By car the 102 km journey will take at least 90 minutes. The trains run every hour. Use Sydney Trains "Trip Planner" to work out how much time you need. Local buses (also using Opal Card) leave every 20 minutes 100 metres down from Katoomba Station. The Three Sisters Plaza/Echo Point is 5 mins away.
The Hop-on-Hop-off Bus is $30 per day - seems too much to pay.
There are a wide range of scenic bush walks (10 mins to several hours if you are a day-tripper).

Suggested itinerary (if you only have a day and you like a good walk with heaps of lookouts along the way)
9:18 a.m. train from Central. Arrive Leura Station (2 hours later). Walk through Leura Village along Leura Mall, follow signs to Leura Cascades (via Blue Mts Drive - BMD brown sign). Walking track (Prince Henry Cliff Track) starts at Leura Cascades car park. From there it's a 90 min walk to Three Sisters/ Echo Point, including breathtaking views of the Jamison Valley (including Bridal Veil Falls). You catch a local bus to Katoomba Station for the 2:14 p.m. train back to Central.
Getting off at Leura (one stop before Katoomba) means you avoid the crowds getting on the bus from Katoomba. Leaving from Katoomba means the train is nearly empty when it arrives.

Trains are comfortable, with first and last carriages designated "Quiet"

Katoomba Station

Jamison Valley from Prince Henry Cliff Track

The Three Sisters