The world museum is fantastic. The round trip ferry is good and it has a german u-boat at one of the stops. The riverfront is worth a visit. The city centre is nice and I hear the Liverpool One shopping centre is really good, although I've not been. Speke hall, near the airport, is a nice National Trust property. You can also go on a Beatles homes tour from there but I think you have to book first. The philamonic hall is meant to be great and Liverpool Empire is a nice theatre. The Catholic Church 'Paddy's Wigwam' is a unique building if youre into thay sort of thing.
My Brother in law is a dipper and dragged me to look at their museum. Even though I felt dirty the whole time, the 5 Champions League/European Cup trophies, lines up in a row is bloody impressive.