Hi,
Exploreing NSW by train is fun and cheap I will suggest a few day trips from Sydney.
1]Leave Central Station for Katooma in the Blue Mountains buses meet the trains and they will take you where you want to go.cost for the day aprox.$20
[You can catch an early train and have a whole day walking and exploring if you want.
2] Wollongong and the South by train . Trains leave every half an hour in peak time and every hour.Leave central station and follow the coast line to the Gong. Beautiful beaches a very senic trip.
Learn to surf and enjoy the rainforest walks. cost apox. $20
[use you day pass on buses they pick up at the station.]
3] Leave central station for the Southern Highlands Mittagone and Bowral. Bradmans Museum is well worth a visit. In September it's tulip time in Bowral. Cost Apox.$20
4]The North Coast Travel to Gosford or the Hunter valley by train have a great day visiting the wine region. cost apox.$20 by train.
5]Visit our National capital by train Canberra You would need to stay overnight. Most attractions in Canberra are free September and October are good months as the flower festival runs for a month free to all a great day out. walk or ride a bike around the lake. The war memoral is free to all just think what you would like to see as it is so large you would need a month to see it all.