The Musuem of Liverpool, this has a carriage from the Overhead Railway as well as an explanation about it, my GC love it, is worth a visit it is by the Albert Dock as is the Tate. The Central Library (recently refurbished) in WilliamBrownStreet (Picton and Hornby Rooms worth seeing) is by the World Museum, also the Walker Art Gallery, the 3 are close together St George's Hall is nearby. If you have time the Everyman Theatre won the Stirling prize a couple of years ago, you could also call in at both cathedrals as they are nearby (Hope Street). The Philharmonic Hall is also in Hope Street as is the Philharmonic Pub (beautiful Art Nouveau building). Trip out to Crosby to see Gormley's statues weather permitting. Not to mention the Beatles, Liverpool FC/Everton, Speke Hall, National Trust Elizabethan Manor House or the 3 Graces.