Getting from Heathrow to Goldsmiith's Hostel in downtown London

If you can't carry the suitcase at all the only answer can be a car service, with a porter at the airport to take your bag from the claim to the car.

Oh, I can carry it, but it's not a little backpack or something.

If you can move the luggage yourself thru the airport, take the Heathrow Express or Heathrow Connect (train) to Paddington Station. Follow the signs to the taxi stand and take a taxi to your hotel.

"suitcase too big to carry" ... "Oh, I can carry it" - confused me a bit. As an alternative to the Heathrow Express / Connect route, you could take the Piccadilly Line to Kings Cross / St Pancras and take a taxi. There is step free access to ground level at that station.

Without luggage it looks like it would be an easy stroll from Mornington Crescent Underground on the Charing Cross Branch of the Northern Line or Camden Town Underground on both branches of the Northern Line. Its a bit of a walk from Euston and Euston Square which are on the Northern, Victoria, Circle, Hammersmith and City, and Metropolitan Line. With luggage you can't carry, taxi. Or get DD to meet you at Heathrow and get her to carry the luggage. That's what kids are for isn't it? Do be advised that your destination is a long way from what most people might define as "Downtown".

This looks like the website for the hostel, same postcode. http://www.viridianhousing.org.uk/find_a_home/short-stay-accommodation/hostels/goldsmiths-house If you put this address in Google Maps you can see the place on Streetview. Goldsmith House
Park Village E, London, Greater London NW1 3SX

Normally I would recommend taking the Tube. However, since you will have a large suitcase and you asked for "the most efficient way", I'll recommend a private car service. The cash fare for a saloon (sedan) provided by Just Airports to anywhere in postal code NW1 is £34. That's much cheaper than a taxi. If saving money is of ultimate importance, then take the Tube. Take the Piccadilly Line to Leicester Square. Transfer to the Charing Cross branch of the Northern Line and take it to Mornington Crescent. Walk to the hostel. For a zoomable map of the Underground system, go here.

I've just noticed that there is a cool 24 hour bus line called the C2 which runs reasonably close to the Hostel. The map and stop list is at http://www.tfl.gov.uk/tfl/gettingaround/maps/buses/?r=C2 It starts at Victoria bus station, runs up to Hyde Park Corner, runs down Piccadilly, turns left near Green Park tube station and goes around Berkley Square, over to Regent Street, crosses Oxford Street at Oxford Circus, up Upper Regent Street into Portland Place and then Great Portland Street, and then Albany Street near the Hostel on its way to Camden Town tube via the Parkway, and onwards north. It looks like Cumberland Terrace would be the nearest stop but you'll have to walk around the Regent's Park Barracks of the Guards. That may be of some help...

The 88 is also nearby which goes through Bloomsbury, down Regents Street, Oxford Circus, Piccadilly Circus, Trafalgar Sq, Whitehall etc. The 23 goes back along the Euston Road and then past Paddington.