London as a whole is VERY safe and you certainly needn’t worry about the Tower Bridge area.
Definitely go on the Uber boat at sundown - great way to see so much whilst relaxing. And there is a bar on board!
The top of a double decker bus is another great way to see so much: routes 15, 11, 9, 24 come to mind. Get a bus map.
You should really see a couple of shows, e.g. The Play That Goes Wrong, Witness for the Prosecution, Operation Mincemeat, or a musical. Check out the TKTS website.
The PROMS are on until (I think) mid- September. Book promming (= standing) tickets for the day online (just £8). Great music and great atmosphere. The Gallery is more relaxed than the Arena. Late night Proms tend to be a bit more ‘edgy’ than the main events.
So many museums…… Imperial War Museum, Natural History, British Museum, the National Gallery…
Good places to eat with several branches that don’t break the bank: Tas, Prezzo, Wildwood, l’Ulivio.
And do wander through St. James’s Park, but try to do so in the morning as it gets busy.