We also need to know the dates of your May half-term (I don't know about you, but we only get a long weekend in Scotland).
If you're quite flexible, you can get them £50-80 one way with your railcard. They're AP tickets, though, so you have to reserve well in advance and ensure you travel on the trains you book for. That could come to less than £100 if you pick the right services.
Your next tickets up are your off-peak only savers, £139.90 RTN but you're really limited on your return services due to the off-peak only restriction.
The best site when using a railcard (particularly a family railcard) is the NXEC site, so give it a go for the dates your selecting.
Really depends on what day/time you wish to travel. Could potentially be done for as little as £35 depending on this. I randomly put in Monday 26th May, and I found advance purchases outward on the 0800 for £17, with the return coming out a little more at £52 (travelling on the 1913 service).
Just to confirm, Fred, I was usipricing from Teddington and a couple of random dates in late May. By purchasing from Teddington, you only have one ticket in each direction which also covers the ourney in the tube should you wish to use it.
Do remember that May Half Term may be different for others; Scottish school holidays are usually different for example. Therefore, no-one can just know the dates where you live.
You've asked me this question a few times, here's the answer again
Using last year's fares (so add approx 6%):-
Teddington to York SVR is £132 for the group. You can leave Teddington at any time but you cannot leave KGX before 0929 M-F. Weekends any time.
CDRs from London to Peterborough and Peterborough to York are £85 for the group on a weekend. Virtually all NXEC trains call at Peterborough so this is ideal for a weekend.
CDRs from London to Grantham and Grantham to York are £93 for the group, or you can split at Newark for about £95. Note that the train must call at Grantham or Newark, respectively. You may need to change at Doncaster. You can leave King's Cross from 0957 onwards M-F.
GC only tickets are £192 from London, and are utterly pointless. If you want to use GC get a Saver.
I find through tickets are generally a waste of time for day trips at the weekend. The only advantage there is for NXEC plus connections tickets from South of the River is you can sometimes get availability when there is none from London.
Myself I generally use a Pricebuster or daysave ticket then Oyster cross London.
Another option from London is via St Pancras. The journey time to York is around 4 hours and the 7.25 departure often has Megatrain or EMT advance tickets available up to the last few days. This train arrives in to Sheffield just before 10 and there is a xc connection to York at 10.20 again with good last minute availability of advance tickets costing only a couple of quid.