My favourite location for hotel stays in London is in South Kensington in the vicinity of the Cromwell Road where it meets Gloucester Road: the Gloucester Rd tube station is adjacent (Piccadilly Line, District and Circle Lines). There is a Waitrose, Tesco Extra and a huge Sainsbury's (they are supermarkets) within spitting distance plus lots of places to eat. I stayed there (again!) just a couple of weeks ago. It's also an easy trip from Heathrow airport.
Just down the street (within walking distance) is the Natural History Museum, Science Museum and Victoria & Albert Museum - so there are some options to take the kids in inclement weather. Kensington Palace Gardens is also within walking distance (15 min stroll) and you can take the no. 49 bus to get to and from there (it goes along Kensington High St). There are a number of bus routes but I prefer to get around by tube train - but it's nice to have a choice and I'm sure the kids would love to go on a London bus!
You can also take the bus, tube or a longer walk along Cromwell Road to go to Harrod's and Harvey Nichols. I was astonished at the number of Arabs taking an evening walk, I guess many come to London to escape the Summer heat back home....I saw high-end cars which included a Bugatti, Ferrari, Bentley, Aston Martin and a Rolls Royce (in Barbie Pink!

) all with Arabic car rego plates parked near Harrod's - they must airlift their cars in for a few weeks...

Anyway......for hotels; in the Gloucester Road Underground Station vicinity the Holiday Inn Forum has a large (and very busy) lobby as US airlline crews stay there; it's a huge hotel with 26 floors - but remember that London hotel rooms, just like in NYC are generally small (Novotel hotels have larger rooms but I doubt you would want to stay in Hammersmith?). The Crowne Plaza is also nearby (lobby size is not as hectic as it's a much smaller hotel, but a decent size). Also there is a Radisson Edwardian, a Bailey's Hotel, next door to that the Singaporean-owned Millennium (Gloucester?) Hotel....with a Bugis Street restaurant lol! but I have no idea of the lobby sizes. I guess you can look them up online.
Also in this vicinity are 'serviced' apartments, including the Fraser ones (again Singaporean owned I think). There is one on the Cromwell Road and also just across the street in a side road; We stayed in a 1-bedroomed Fraser apartment in Queens Gate Terrace (on the corner of Cromwell Rd) a couple of years ago, but I didn't like it much , I prefer to stay in an hotel! However, there is a laundrette just a few yards from Sainsbury's on the Cromwell Road and it was much cheaper than using the hotel laundry service (and they will wash and press shirts to collect a day or so later).
TBH I would never let a small child wander around an hotel lobby (or anywhere else) unless he/she is very closely supervised - it's too dangerous in case of accidents or abduction (and there are paedophiles all over the world, not just London....
