Northern Ireland is known for its Norman Castles, monuments, valleys and mountains. It is easily accessible in 2-3 hours by ferries from Liverpool and Cairnryan. Or you can also get a ferry from Holyhead to Ireland and then take a bus to Northern Ireland (given your visa allows it).
Giant's Causeway is a national trust site located on the north coast of Northern Ireland.
#Travel hack - If you are planning on visiting the UK, you could consider getting a national trust membership. That way, you can visit a lot of places and save a lot on entry fees.