Everton (h)  Saturday 9th March 3.00pm

Note that the 1904 is the last train from Newcastle to York. After that you have to get a bus part or all the way. Here's a selection of train times, with fares as at 28/01:
 Leeds 0852 0908 0912 0921 0939 0952 1008 1021 1039 1051 1108    Toon 1717 1732
1744
1803 1815 1836
1844
1853

1904

 York  a 0916 0930 0934 0943 1001 1017 1030 1043 1101 1117 1130    York a 1822 1831
1840
1907 1920 1933
1940
1957

2001

 York  d 0918 0931 0948 0955 1002 1018

1032

1054 1102 1117 1132    York d 1823 1841
1845
1909 1922  
1945
2009

 

 Toon 1022 1029 1047 1052 1107 1126

1129

1150 1208 1224 1231    Leeds 1846 1905
1909
1932 1946  
2008
2032

 

 From Leeds 24.70 30.70     30.30 30.30 30.70   30.30 30.30 30.70  

 To Leeds

30.60   23.85 30.60 30.60   18.30 30.60  
 From York 7.50 18.20 18.20 15.50 18 18 18.20 15.50 18 18 18.20  

 To York

18 9.95 7.55 18 18 7.55 7.55 18 15.50
1234  Transpennine         2345  Cross Country         0123  East Coast         3456  Northern
 
These are the fare options from Leeds:

From 31.20

 Off Peak Day Return Leeds-York (any trains), Advance Singles York-Toon

From 43

 Advance Singles

44

 Off Peak Day Return Leeds-York (any trains), Off-Peak Day Return York-Toon (TransPennine trains only)

57.70

 Off Peak Day Returns Leeds-York and York-Toon (any trains)

62.40

 Off Peak Return (any trains)

And from York:

From 15.50

 Advance Singles
28.30  Off-Peak Day Return (TransPennine trains only)

42

 Off Peak Day Return (any trains)

Notes:
1. Railcard holders can get one third off the above prices.
2. 16-25 Railcard holders can get 50% off TransPennine fares if booked at www.tpexpress.co.uk.
3. Groups of three or more can get one third off TransPennine fares if booked at www.tpexpress.co.uk.
4. Groups of three or more can get 25% off LNER fares if booked at www.lner.co.uk.