99% correct, the exception for free museums is The Natural History Museum which can attract long queues, especially at weekends and school holidays but outside of those times (and later in the day) no problem.
I suggest you pre-book your (free) tickets here, before you go.
They put this in place to try and manage crowds and last time we were there we were in a short queue and fiddling with trying to book the free tickets on a phone before we got the end of the queue. No great hassle and no great wait but it is one little task you can do over breakfast that might just save you a ten-minute wait at the entrance itself.
Two other free things that I always highly recommend for London visitors is
a) The Skygarden. Across the River from the Shard and overlooking the Tower of London, nice food and a nice place to soak up the views. Free of course and you just need to book a time slot in advance.
b) Grant Museum of Zoology, Part of UCL it is like stepping into the laudanum dream of a Victorian gentlemen naturalist. Again, all free.
The other main free museums that I recommend you shouldn’t miss are
The National Gallery
Tate Gallery
Tate Modern
Victoria and Albert Museum
British Museum
Science Museum
The Museum of London (though I think it is closing for a little while whilst it changes location, not reopening for a couple of years so forget that)
The main Museum of London closes in December before re-opening in grand new premises in a couple of years, but its Docklands sister will still be open. And from there you can go on to Greenwich
You forgot one of my favourites, the National Portrait Gallery. Art and history combined, lots of bang for your free buck. It’s closed for renovations at the moment but will hopefully reopen in time for the OP’s visit. Bound to include a special exhibition on our late Queen.
I’ve never actually been to that one, portraits aren’t my thing, but I’ve heard great things from those who’ve been.
It is right next door to the National Gallery and situated just off Trafalgar Square. there’s a full day’s entertainment right there. Get lost in both museums for hours, stroll out into Trafalgar Square and toddle off down Whitehall to Parliament square.
Downtown equals “city centre” for all intents and purposes, and in most US cities denotes the area where the primary governmental, social and commercial activity goes on. Here in Dallas, “downtown” is the central business district where the skyscrapers are, and where the better part of the City government, the County government, and the Federal government presence is (Federal building, Federal Reserve Bank). It’s also where there’s a lot of office space and a few large companies (AT&T is headquartered there for example).
Uptown is a bit more nebulous. It generally means a more or less built up area with a lot of social and commercial activity that’s near, but not actually within “downtown”. Uptown Dallas is basically adjacent to downtown- the Federal Reserve Bank is on that border in fact. It’s more of an area of bars, restaurants, apartments and retail.
London’s big enough and decentralized enough to where I’m not sure that “Downtown” really applies. I mean, Canary Wharf is where the skyscrapers are, City Hall is in Southwark across the river, the governmental stuff is in Westminster, the “City of London” is downriver a bit, and so forth. There really isn’t a “downtown” exactly like you have in a lot of other cities- maybe everything inside the inner ring road is “downtown”?
No there isn’t, in large part because London is effectively a collection of cities - City of Westminster (where business of government… and shopping and culture, in large part happens), City of London (original roman city, where the finance and law stuff now happens) and City of Southwark, (where local reprobates like Shakespeare hung out, away from the clutches of City of London laws and where the Mayor now does his business.)
That’s the long way round of saying that no, London doesn’t have a ‘downtown’ or city centre in the traditional sense. It’s often called a collection of villages.
So London doesn’t have a single centre. Charing Cross, next to Trafalgar Square, is pinpointed as the centre according to road signage makers, but that doesn’t count for much.