London neighborhoods summed up?

Knightsbridge--Home to Harrods, mixture of residential and some tourist. Upper/Middle Scale.

South Kensington--residential with some hotels, middle, some museums, (I like this area.)

Belgravia--residential--the rich, embassy's, mostly residential with higher end hotels.

Chelsea--upper/middle, trendy, residential

Mayfair--see Belgravia

I'll leave Marylebone (newly found chic) and Lancaser Gate to others as I've never stayed in those areas.

None of the areas you mention are particularly ethnic so you'll find all types of restaurants.

London is a very easy city to manage. If you're there for a week, pick a neighborhood you want to stay in, and expect to travel outside that area. The tube and buses are convenient to everything. None of the main attractions are in any of the areas you mentioned as they are more residential than tourist.

Most of the areas you name are pretty upmarket. South Kensington and Lancaster Gate a bit less. Lancaster Gate is close to a really major traffic artery so there may be a bit of issue with noise/air/kid-safety.

The most kid friendly is South Kensington: you're close to the Natural History and Science Museums. Marylebone has Madame Tussauds, but that's the most notorious tourist trap in London and no resident would recommend it. Belgravia and Mayfair can be a bit sterile, are short on attractions, and you're unlikely to find any but the most high-end businesses.

Chelsea is fairly upmarket but a bit livelier (don't expect to see any actual punks nowadays there), but has the disadvantage of being a bit less well served by public transport than your other choices: frequency is still good but it will take longer to get to other places of interest.