Originally Posted by
redtailshark
You will need to choose an attraction that is close to a convenient HEX terminus with minimal tube riding.
I would not recommend taking Heathrow Express at all. It gets you into Paddington. There are no major attractions near Paddington. By the time you have queued for a taxi and driven to a major attraction, you would already have had time at that attraction if you had gone there by Piccadilly Line. Plus, you would save yourself many £££ by taking the tube.