Advice on how to get from Heathrow Airport to Grosvenor Hotel in London?
Kathy is correct. Thats the best way to get from Piccadilly Line to Victoria Station
The Piccadilly Line doesn't go to Paddington Station that was wrong information. Kathy is right take it to Hammersmith and change to the District Line to Victoria Station.
The nearest tube station is Victoria. My route would be to take the Heathrow Express to Paddington and then take a taxi from Paddington to the hotel. (You could get the Circle line round from Paddington to Victoria but with luggage, exhausted etc I would rather get a cab drop me off right at the hotel. Getting out at Victoria, if you dont know the area, can be hard to orient yourself.)
If the Grosvenor Hotel is the old Victoria Thistle, then take the tube (Picadilly line) from Heathrow to Paddington, then change to the Circle line to get to Victoria station. The hotel has an entrance right inside Victoria station as well as one on the road (around the corner). We have stayed then many times and enjoyed it.
The Piccadilly line doesn't go to Paddington. Take it to Hammersmith and walk across the platform to change to the District line to Victoria. See http://journeyplanner.tfl.gov.uk/user/XSLT_TRIP_REQUEST2?language=en
Follow Kathy's advice if you're awake, alert and want to pinch pennies. If you're exhausted, hazy and jetlagged, and/or have multiple pieces of luggage, take the Heathrow Express to Paddington and then a cab to your hotel.