I believe that the Docklands is the Hilton with the worst connection into Heathrow. You need at least two changes (Ferry or hotel bus to Jubilee line, Jubilee to Piccadilly line OR hotel bus to Jubilee line, Jubilee to Bakerloo line, Bakerloo to Heathrow Express). I normally pay 45 GBP for a car service from my office in Canary Wharf (very close to the Docklands Hilton) into Heathrow.

For your purposes, either the Hilton on the aiport or the Paddington Hilton or Metropole Hilton, both in walking distance to the Heathrow Express train HEX would be the best choice. The Metropole might be the cheapest alternative.