I'd say definately the IWM, BM and personally I'd want to visit the Natural History Museum too. HMS Belfast and Churchill's War Rooms also are a must, as is Victory and the other Gosport/Portsmouth museums.
Regarding Stonehenge - yes it is impressive how the stones arrived there and the questions of why/how/when, but there are a couple of points -
The A303, the main road past is notoriously jammed - nothing to do with the stones but it's one of the main routes to the S.W. of the country from London, it's dual-carriageway up to Amesbury (where I used to live/work for a couple of years, so I'm talking from experience) and then single for the next x-amount of miles past the Henge. It has a permanent fixture on Sally Traffic's Travel Reports on BBC Radio 2. 
The actual site at Stonehenge is tiny, always looks massive on the telly, but it really is disappointingly small - about 100' diameter. I'd rather go to Avebury, a village surrounded by stones - about 1300' diameter - and it has a nice pub near the middle. Also not far from Avebury are some prehistoric mounds and the like, as well as the fabled White Horse chalk drawings on the side of hills.
As for when you should come, the 2012 games finish on the 12th of August, and the Paralympics on the 9th September so I'd try for after then, you've also got the advantage of the kids being back at school, and it's usually still good weather.
I've never had a problem getting around London using the Tube, and I'd recommend that over hiring a car in the city - save that for your excursions farther afield. Another must, and I think if possible we should get quite a few of us together, is a Sunday at The Church
http://www.thechurch.co.uk/ I've not been since it's moved from Kings Cross but if it's anything like it was it is a brilliant, if a little bit drunken, few hours of your life.
I think I'd be able to pop down for a day or two for a museum or two, I'll bring my doggy snacks
