Not sure what the "price" difference is vis a vis points, but the HI's around Victoria Station would likely be most convenient or the ones in Mayfair or Kensington. There are also a couple of Express properties, also near Victoria Station and a new one a few blocks from Hammersmith Tube station. This one would be on the Picadilly Line to LHR, and is in a local neighbourhood which might offer a taste of London most tourists don't see. They have converted the old Fuller's Brewery for this property. Have no first hand experience with any of these, though. Also a couple of CPs, but these are likely quite "pricey". Suspect you'll be looking at 25K for both HIs and CPs, so CPs would present the best cost/value. Express locations would be 20K, and ICs 30K.

Real issue is how long your overnight in London is, and how early you must be at LHR for your return flight. Then look for a location with good proximity to Picadilly Line or the AirBus, or if you feel flush, getting to Paddington for the Heathrow Express.