What do they enjoy?
When I used to visit London for day trips as a teenager (I skived off sixth form college some Fridays on my own, caught the National Express from Bath, for no other reason than just because) I used to mooch around Camden Market because it felt like the epitome of cool then; I wandered each of the Magnificent Seven cemeteries; I did a solo Jack the Ripper tour to locate all the locations of crime scenes and where the victims had lived; I went to the Imperial War Museum (it was better a decade and a half ago, but still worth a visit); I tried to find all the locations along the Thames where pirates had been gibbetted in days gone past; I ate the cheapest Chinese food I could find in Chinatown.
Granted, I still love to do all of these things nowadays, even now I’m 35 and live in London. But obviously they’re no good if your teenagers are into fashion, or gaming, or finery.