would like to go travel for 1 & half days from liverpool, where should I go with low budget and how?

For an excursion into the countryside: You could take a train to Betws-y-Coed (about 2 1/2 hours away, £17 fare). Visit Snowdonia National Park and stay at a YHA youth hostel (Pen-y-Pass is ideally situated and only £14 a night). It's a beautiful area- and a nice break from the pace of city-life.