The best cycle trail in / around Liverpool has to be the Trans Pennine Trail - it is a mainly off road trail and stretches from Southport on the West coast to Hullon the East coast covering a route that can take in Liverpool, Manchester, Barnsley, Sheffield, Leeds, York through spectacualr countryside and some  surprisingly beautiful heavy industry near Warrington.  It runs along canal tow paths, old railway lines and purpose built trails.  So there are parts of the route that are suitable for any age or cycling ability.

There is a website http://www.transpenninetrail.org.uk/ that has all of the details - enjoy.

Another vote for the Trans Pennine Way, it's a fantastic route. In and around Liverpool is quite difficult to find good traffic free cycle routes, but one of my favourite rides is to join the Mersey near the Otterspool Adventure Centre then cycle northwest on the cycle lane next to the river to the city at the Liver Building.

For something longer, I tend to continue north to the beaches at Crosby Beach, Formby, then on to Southport.