Need help finding locations for 2 flat rentals for summer 

I will be traveling with my 15 year old son for 2 weeks this summer in England, but before the Olympics (early July) hoping to miss the huge crowds. I have finally decided to rent a flat for one week in London, and then another week in a central touring location in the countryside. Please help me figure out the best spots for both. In London, I would love to be in a safe area which is in walking distance to many attractions. I have never been to England at all, so I feel like I am guessing... but would Kensington or Chelsea be good neighborhoods to look? Or another? Also, which area outside of London would be a good central spot for day trips to the standard attractions, i.e. Stonehenge, Cotswalds, Liverpool, Stratford-on-avon, etc. and is a destination within itself? I would love to feel the character of England in both locales. Thanks in advance for any advice!