The best London bus route passing the Tower of London (it starts in the East End of London) is #15 to Trafalgar Square. If you change there within 1 hour of boarding at Tower Hill you get a free transfer onto #23 (to Westbourne Park) down Regent Street and Oxford Street to Marble Arch (and Paddington).
Anywhere on Oxford Street switch to #10 which takes you to Harrods, Royal Albert Hall and Knightsbridge (#9 takes you straight there from Trafalgar Square past St James' Palace and Green Park).
Switch at Marble Arch onto the #74 and it takes you to the V and A, and the Natural History Museum.
You get an unlimited number of free transfers within an hour of boarding.
But any of those are easy and wonderful sighteseeing routes for the princely sum of £1.75.
Stay on the #74 to Putney and you can catch a Thames Clipper boat down the Thames back into Central London. It is not included in the daily/weekly cap, but can be paid for using Oyster or contactless.
(or catch the Clipper from the Tower to Putney then reverse the bus travel).
That is a wonderful half day touring for a fraction of the cost of the HoHo.
Lots of similar possibilities on the service buses.