At the moment there is a Bodies Revealed exhibition on in Liverpool One, I’ve not yet been but friends and family have and all gave positive reviews.
As mentioned above there is lots of beautiful architecture so remember to look up when you’re wandering around. If you get a nice day then a trip to the roof of the cathedral (Anglican, big sandstone one!)is worth a go, only costs a few quid. Then walk along Hope St to the other cathedral. Lots of restaurants along Hope St. The Quarter on Falkner st is one of my favourites for a chilled lunch, or the Side door is good too.
Albert Dock and the Tate are good for a wander and the new Liverpool Museum at the Pier Head although I can’t testify on that as I haven’t been yet.
If you want anymore specific advice just let me know.