You will be able to use Mersey Rail to access Liverpool - check their website. Lots to do in Liverpool, check out the website www.visitliverpool.com.
You don't say what your interests are so difficult to know what direction to point you in.
I was in Liverpool a couple of years ago for the galleries, architecture etc. Visited the 2 cathedrals; the galleries and museums around the Albert Dock (Tate, The Maritime Museum, Slavery Museum etc); went to the Walker Gallery in the centre; other really interesting buildings in the centre. Terrific. There are Beatles tours if that's you're thing. The guide on one of the tours I took noted that, after London, Liverpool has the most Grade 2 listed buildings in the UK.
As you are north of the City you could have a quick stop off the train at Crosby and see the Anthony Gormley installation on Crosby Beach - called "Another Place". I went one really wet afternoon in late September, very spooky and atmospheric - I loved it.