Was coming to suggest this - Jack the Ripper walking tour was a big hit with my Year 8 students when we did it last year. Very entertaining, a bit creepy, and also really interesting to see how much of the area has stayed the same and how much has changed.
There are loads of great evening walking tours available in London, OP, many of which are suitable for teenagers and only last an hour or so. With the lovely weather we're having at the moment it makes sense to be outside if you can.
Tate Modern is open late on the last Friday of the month - not sure if that will coincide with your visit.
Greenwich is amazing in the evening - lots of nice restaurants, gorgeous walks along the river, and you can walk under the river in the foot tunnel if you like and get the DLR back to Tower Gateway from Island Gardens.
Canary Wharf also has loads going on in the evenings - there's a mini golf place there now and loads of shops and restaurants that stay open late, as well as nice walks along the river. Again, easy to get to by DLR from Tower Gateway station which is right by your hotel.
Shoreditch BoxPark is a good place to get street food and there's a place near there that does crazy golf as well - https://tedscrazygolf.co.uk/london/
IMAX cinema at Waterloo is well worth a visit.
Please don't worry about safety. London is so so safe. I'm born and bred, lived here nearly all my adult life, never had any issues with safety. I sometimes have to do volunteer shifts that finish in the early hours of the morning and I walk home without a worry at 3am. The streets in central London are busy all night long so you're never going to be in a situation where you're alone and vulnerable - there are always people around. I feel more unsafe in the countryside at night than I do in London!
The Tower Bridge area is totally safe and it will be busy at night - there are lots of pubs and offices and so on around there so always people milling about, plus loads of tourists. Get out and enjoy the beautiful river views at night and walk as much as you can. Don't waste money on taxis and Ubers!