London is not a big place, in the sense that it is not an urban sprawl, especially for the places you may want to sightsee on your first visit, but it’s also not walking distance between all the major attractions. Well no, that’s not really true, you could do it, but if you are here for a limited time, you want to make the best of the time you have and interminable walking is not the thing to be doing.
It’s best to have a plan, and to be realistic in that, you’re not going to see everything. Listen, on and off I have lived here for 40 years and I haven’t seen everything (whatever that means). There are always hidden gems, and things changing (and also stuff to avoid like the plague).
So, do your research and have a plan. Make a list of must see places, and then see what other things there are in the same area.
For example, if Tower of London is on your list, see also Tower Bridge, the river, the Bank of England, St Paul’s, the Monument… thie list is endless. Be prepared to queue, and allow time to just amble around to look at the world and soak up the atmosphere. A holiday where you dash from one place to another, tiring yourself out and barely remembering what you saw, is not, in my opinion at least, a holiday, certainly not restful.
I know people who visited London a few years ago and top of their list was the Natural History Museum. They spent their first day there. The next day they went back. The next day, the Science Museum, and so on. And they absolutely loved it. It was something they did not have at home, it was free (actually) and they had a great time.