Depends what they are interested in.
We had a great time in the Highlands with older teens - bagging Munros, went kayaking, hiking.
Same in the Lakes - lots of hiking, water sports, bagging Wainwrights etc.
Bristol is good for doing a Banksy trail and other really good artistic graffiti, riding the river bus, independent shops, museums etc.
London is always good for shopping, people watching, quirky or cool museums, good street food and street entertainers, gigs and good tourist activities like riding the cable car, climbing the O2, Clipper boat, DLR etc.