Big Boy, it depends on where you live. Since you have fished Newsham Park (the place I caught my first fish) I am guessing you can access the main circular bus routes fairly easily. 26 takes you to Sefton and Princes Parks both of which are OK - but don't go alone to any of the public parks.
Take the 68 to County Road and then any bus out to Old Roan or Maghull for Liverpool and District stretches of the Leeds-Liverpool Canal - You will need an L&DAA card first though - most local tackle shops have them.
It is also possible to get to St Helens by bus to fish the Church Street Canal, Leg-O-Mutton Dam and even Carr Mill Dam. Again you need a club card and obviously travelling costs (and time) will mount - but I used to do it every weekend when I was in my teens! Good Luck!