Normally I'd suggest one of the Thistle hotels, but the obvious ones (Tower, Kensington ones, Westminster, Victoria) are coming in about £100 per room for B&B. If you really want to do sight-seeing, then I would suggest staying in London somewhere, but preferably either close to Paddington (for the heathrow Express) or on the Picadilly tube line (again for access back out to Heathrow). Have a look at Expedia - they have a pretty good range of hotels for London.