(2-part post):
Thanks for the reply. You've got three big problems in seeking cheap rail fares:
1: The cheapest fares generally aren't available at peak times, which make them difficult to find for day trips.
2. It's a bank holiday week, when cheap tickets usually sell out very quickly.
3. It's incredibly short notice. (You need to book a couple of months in advance for the best fares).
Looking at a rail map, and seeking inspiration for somewhere to go for a day trip from York, it occurs to me that Durham is a very pleasant city:
http://www.google.com/url?sa=t&source=web&ct=r es&cd=13&url=http%3A%2F%2Fwww.durhamtourism.co .uk%2F&ei=AfL9SZaRA4e5jAed8ZSlAw&usg=AFQjCNFvA aanxAuh9lEm-T226joiqJxV4w
The full return fare from York is �50.80 but off-peak travel (which seems to be available on most, if not all, trains) costs �32.50. If you're prepared to travel at some rather odd times (such as out at 0706 on Thursday and back at 2200), you can get the fare down to �21.00. (In practice it might be better to pay �24.50 and return earlier, such as on the 1836 departure from Durham).
Closer to home, Harrogate is well worth a visit:
http://www.harrogate.gov.uk/harrogate-266
With 'walk up' Anytime Return tickets costing just �8.30 you wouldn't have to worry about seeking advance travel on specific trains.
From time to time I make trips (all the way from Suffolk) to visit the National Media Museum, in Bradford:
http://www.nationalmediamuseum.org.uk/
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