You dont say if you have the night there, or just the Saturday.
If you have just the Saturday then as has been said, the day will just fly by.
If you want shopping then Oxford Street is the most obvious. Selfidges is an amazing shop to go in.
If your 14 year old has not been to London then the best "sight" to see is possibly Trafalger Square, as there is always a lot going on there.
Also Covent Graden has loads of street entertainers, as well as lots of market stalls selling Jewellry and so on, so that will be interesting for a 14 year old.
Or maybe Hamleys the toy shop on Regent street, or Harrods, which has an amazing toy department (both of which will be of interest to adults as well).
And Bond Street (just off Oxford street) is where the rich shop, loads of expensive watches and jewellry. You see more Rolls Royce's in Bond Street than any other street (not a fact but my observation).
Piccadily Circus and Leicester Square are both worth a visit as they are "free" but there is a lot going on there.
Also, is the Trocadero still open just near Piccadilly Circus?
It was full of shops, places to eat, cinemas, even fairground rides the last time I was there. Nearest thing in London to an indoor theme park, but I think it may be being redeveloped at the moment.