Well you will be right in the city centre so shopping, eating and drinking will be all around you! Beatles experience, Magical Mystery Tour, strange amphibious yellow duck bus (never been on it but apparently after driving around for a bit, it then launches into the Albert Dock), Ferry across the Mersey, complete with Gerry Marsden soundtrack (well it was the last time I was on it!) plus all the museums and art galleries.
A bit further afield (short bus ride) you've got Speke Hall, Knowsley Hall, Croxteth Country Park, Sefton Park (and it's glorious Palm House)
I'm sure I've missed loads out - and you're within a couple of hours of North Wales, the Lake District and Yorkshire! Where are you travelling from?