What are the most worthwhile things to do in London on a first visit?

London's visitor economy splits cleanly in two, and understanding the split is most of what a first-timer needs. On one side are the ticketed, timed, capacity-managed historic sites. On the other are the national museums, which are free at the door. A first trip that spends money on one or two of the former and time on the latter gets far more out of the city than one that buys everything.

The Tower earns its place on the paid side. UNESCO lists it under cultural criteria (ii) and (iv) — criterion (ii) covering the interchange of human values and influence a property represents, criterion (iv) covering an outstanding example of a building type. What you walk through is a concentric medieval fortress, with a Norman keep at the center and successive rings of wall built outward around it, rather than a single building with a single highlight.

The British Museum is the obvious free counterpart, and a small amount of logistics makes it much better. The main entrance is on Great Russell Street, London WC1B 3DG, but there is a second entrance at Montague Place, London WC1E 7JW, which is usually the quieter of the two. Advance booking is required only for groups of ten or more, so an individual or a family can simply walk in. That combination — no ticket, no slot, two entrances — is what makes it the right thing to have in reserve on a first visit, when plans change hourly.

The Tower sits low. Approached from Tower Bridge Approach, the outer curtain wall runs along the river at little more than rooftop height, with the glass towers of the City rising directly behind it, so the fortress reads as a sunken stone enclosure pressed between the Thames and the financial district rather than as something commanding the skyline.

The £37.00 adult figure is quoted excluding the voluntary donation that Historic Royal Palaces invites on top, which means the number you see at checkout may be higher than the number you planned for. That is a genuine budgeting point for a family: two adults and two children at the stated rates come to £111.00 before any donation is added, which is why most first-time itineraries can only justify one site at that price level.

• Buy one, not four — Choose the single paid historic site you most want, at the stated £37.00 adult rate, and let the free collections carry the rest of the trip.
• Use the side door — Montague Place, WC1E 7JW, is the British Museum's second entrance and the one most visitors never find.
• Travel light — At a timed fortress site with narrow stairs and wall walks, what you carry decides how much of it you actually see.

Child pricing cuts off at 15, so a 16-year-old pays adult rates at the Tower — a detail that reshapes the budget for families with teenagers. The fortress is a working medieval site: gradients, cobbles and spiral stairs are intrinsic to it and cannot be engineered away. And the free museums are free precisely because they are busy; the British Museum's group rule means that although you need no booking as an individual, you will be sharing the galleries with parties of ten and more who have booked. Entry to the country adds a step rather than a barrier: no visa is required of a US visitor for a stay of less than 6 months, and the passport needs only to remain valid for the duration of the trip with at least 1 page free for stamps.

The London when-to-visit question in this group sets out the Tower's opening hours and the 15:30 last entry slot, which determines whether a ticket at these prices is usable on your chosen day.