I just ran across this 25 year old post from Ben Haines who I remember as a prolific and authoritative poster. Here's what he had to say 25 years ago when asked a question about London's neighborhoods (for tourist purposes).

"Fodors London Areas

This is quite a challenge, but here goes.

In my view, Earls Court, Paddington and Kings Cross are too far out to be close to the "hub". That leaves the following, going round in a clockwise direction.

South Kensington. Quiet, main hotels rather far from the few shops, plenty of restaurants at the tube station, contains four great museums

Bayswater. Trendy, plenty of rich Arabs and thus a big range of restaurants and in fact pubs too, many shops, mixed hotel and residential area, tube stations at Bayswater and Lancaster Gate, near to Hyde Park and Kensington Palace, but far from most tourist attractions.

West End. Trendy, noisy, full of shops, restaurants and pubs, crowded at weekends, tube stations all over, near Royal Academy, the theatres, National Gallery, National Portrait Gallery, Transport Museum, Theatre Museum, and Westminster.

Bloomsbury. Mostly hotels and colleges of the University of London, fairly quiet but well used far into the night by tourists and students, many restaurants, but better value restaurants 300 yards east on Lambs Conduit Street, plenty of tube stations, area includes the British Museum, the Brunei Gallery, and the British Library

The Strand. Contiguous with the West End, and has much in common. But the handful of hotels on the Strand, Aldwych, and Villiers Street seem to me in the best position of all, with many tourist attractions within a quarter mile, and nearly all the others a few stations away on the Circle Line.

Waterloo. Coming up, but still pretty dull. Quiet, few shops but a number of restaurants, residential, poor tubes but good busses north over the river to most tourist attractions (notably Westminster), and has its own attractions: the three South Bank concert halls, the National Theatre and National Film Theatre, the big wheel (the Eye), and a riverbank walk of half a mile to the Tate Britain and the Globe.

Victoria. South of Victoria station is an area almost wholly given to cheap hotels, with pubs, shops and restaurants to match. Like Bloomsbury in that it is well peopled until late at night, but has plenty of quiet streets. Victoria station is good for tubes and busses, and for trains to the sturdy towns, the gardens, and the fine countryside of Kent. Nearby attractions include Tate Europe, the Queen's Carriages and the Queen's Gallery at Buckingham Palace, St James Palace (much nicer than boring Buckingham Palace) and St James Park, one of the best.

You mention Chelsea. But are there hotels there ? Anyway: trendy, expensive, active, many expensive shops and restaurants with an international and yuppie clientele, no tube stations, so you take busses to Sloane Square and then carry on by Circle Line. Attractions are the Museum of Army History and the Physic Garden.

Nowhere in any of these places is unsafe: you should stay away from none of them. Some three miles out of town in several directions are large estates of apartment blocks, social housing, where the police walk in pairs. But they are ugly, and no tourist is ever there."

So, is this still fairly accurate? Or, have things changed a lot in the past quarter century?

My take -- Earls Court, Paddington and Kings Cross are definitely not 'too far out' -- Generally just about any neighborhood within the Circle tube line is considered central London with the addition of a couple of areas south of the river which are central but not inside the Circle. (disclaimer -- I personally generally avoid Earls Court and Paddington but that is mostly a hold over from how they were years ago -- not how they are now). Kings Cross has probably changed the most of any central neighborhood -- many hotels at all price levels, a huge amount of redevelopment with trendy shops, restaurants, LightRoom, Coal Drops Yard and the Eurostar now serving St Pancras instead of Waterloo.

Sort of weird that Ben thought Paddington is too far out when it is actually more 'central' than Bayswater.

True, there aren't many hotels in Chelsea but South Kensington and Sloane Square are contiguous and there are lots in those areas.

Waterloo has lots of hotels from Premier Inn to Marriott County Hall and decent transport options.
Victoria has changed a LOT in the last 25 years -- there still are budget hotels but several much higher end one as well.

Thanks for your evaluation. I, obviously, am still looking for hotels for a stay.

What is your budget and what sort of property/vibe do you like? There are hundreds and hundreds of hotels in central London (well over a thousand) so searching can be 'crazy making'. . .

I'll preface my advice in that I lived in Bayswater many years ago and recently revisited the area of our flat and I would say the area is very busy! I wouldn't personally stay in that area now but I'm not looking for that vibe these days. That said we have stayed in various other areas of London in the last few years -- Bloomsbury (The Montague), Covent Garden (the Melia), and South Kensington (The Bailey). Of those we found South Kensington great for tube access, restaurants and walkability. Depending on your budget and as Janis says - your vibe -- there are tons of options. I am not a fan of Earls Court, Paddington, or Kings Cross- probably my bias from earlier days. London is so easy to get around between tubes, buses, taxis, etc. - and it is ever changing. Lots of development and revitalization. If you're near a tube stop you're good.

Kings Cross has changed so much in the past 25 years. It used to be made up of crappy little cafes and tiny back streets. Well the revamp of the three main station areas and one glorious hotel the place has rocketed to being a destination in itself.