Depends on money I guess. If you go east ( looking at the tube Map) this willbe more expensive but will be nearer to lots of other things. Ken high street is good for shopping. I reckon you'll find the best selection of reasonably priced hotels near Earls Court as there are always lots of trade shows there. You'd have a lot of fun staying in South Ken as all the museums are good. Also it means you can go to one for a couple of hours, go off to Hyde Park or. The Diana playground in Kensington Gardens and then do some more museum time later on. Also close enough to go to Harrods for treat ice creams etc..... Have fab time.
Is there anyl reason you want to "be there" op? Tube rides are usually part of the fun of London and aren't much in the way of time and effort.
We stay at the Park Plaza which has a superb view of Big Ben and the London eye seeing as it's on Westminster Bridge.It also has a pool and pretty lights in the lift etc and a fab breakfast. There is also a deal tobe had if you phone direct!
It's a walk across the bridge to Embankment and then 3 stops on the District and Circle line to all the museums.
Also my son wasn't impressed with the Science museum - all style and no substance. A lot is interactive but all at the lowest common denominator stuff. Don't go when it's busy because you won't get to use/see the units. There isn't much signage so you can't read as you go along or understand properly what you are looking at. He liked the Natural History and the V&A better just because they have a better lay out I think.