One thing you can do for free in London is to walk along the South Bank of the Thames after walking over Tower Bridge (you are going to the Tower I see) and taking in all the sights along the way. The Globe theatre, historic riverside pubs, HMS Belfast moored along the river, The Golden Hind in dry dock, Statues, small parks, the Tate Modern London Eye/River cruise jetties- much much more, and with the North side of the city always in full view. All on the way to the Imperial War Museum. On good weather days there are amusing street performers and musicians and always street food sellers. If you keep the Thames on your right , when you get to Westminster Bridge turn sharp left and walk towards Waterloo and The Imperial War Museum (you have basically walked a more scenic route right around it) But if you get fed up ANY of the bridge roads turning left will take you to the IWM. (look on the map to see what I mean)
I would strongly suggest you do those three things in one day in that order (Tower of London in the morning, walk along South Bank and IWM for the afternoon. That would be a good and full day you would see and soak up a lot, don't try to add any more. Numerous places to eat at any time along the way, I can recommend the Cubana restaurant near Waterloo as good not too expensive
https://www.cubana.co.uk/find-us/