Well, you have the Beatles stuff covered, and the Ferry, so here are a few more suggestions (non shopping)
Tons to do on the Waterfront - there's the Museum of Liverpool which also has a Beatles exhibition on at the moment, and also the Maritime and Slavery museums on the Albert Dock. Albert Dock itself is nice (though shops a bit tacky and touristy) and you will be there anyway for the Beatles story, so worth a look around - and there is the Tate Gallery there as well.
St George's Hall is spectacular, and there are also guided bus tours which are actually really interesting (I am from Merseyside and even I learned something - like that Hitler once worked at the Adelphi hotel bar (allegedly). Both cathedrals also beautiful though might be a bit boring for teenage boys.
Great parks - Sefton Park and Calderstones Park - the latter has the Palm House with the ancient Calder Stones - and if you go out of the city centre to Crosby beach there are the Gormley statues looking out to sea. Similarly in St Helens (about 12 miles away if you have a car) there is The Dream statue which is worth a look.
Tons of nice places to eat and drink - I would definitely recommend Lark Lane which has some quirky shops (they must allow you one or two) and a great variety of restaurants and bars. Keith's is a local legend (remember it from my student days - a long time ago) and still great. If you want to go a bit more upmarket both Maray and Salt House Tapas are fantastic. For a traditional pub, try Ma Boyles.
Two theatres - Royal Court and the Everyman - which might have something on, and there's the Echo Arena of course so you could check out who is playing there.
If you are on a budget there is a blog called the Poor Man's Guide to Liverpool. Think it is aimed at students but some good stuff on there.
If you get good weather, get over to Wirral and visit West Kirby beach - when the tide is right (do check) you can walk over to Hilbre Island and back in a day which is well worth it. There is also a beach at Formby which has a red squirrel sanctuary
Hope you have a great time.