I need to get from Heathrow Airport to London's Little Venice district after a flight from San Francisco. With moderate luggage and being a bit tired, is the London Underground a good option or are there better alternatives mindful that taxis are prohibitively expensive?
Heathrow Express / Connect to Paddington then a taxi might be an intermediate cost, depending on how many there are of you.
I'd say the Tube from Heathrow (Piccadilly - dark blue) to Warwick Avenue (Bakerloo - brown) is a very sensible option, and what I would do. A Black Cab for that journey could be £50+ easily. Under a tenner on the Tube.
It's a bit of a tough journey though, simple enough, but a long one. With only one change at Oxford Circus (busy, busy, busy!) you might be arrive in 60-70min. But this will depend on your time of travel.
If during rush hour, you would be better to make two changes, and avoid Oxford Circus.
Can you tell us your arrival time at Heathrow and which terminal? (don't worry, we won't come to meet you!)
As above, Heathrow Express is definitely another option, but I've heard it's expensive also.
My personal recommendation would be Heathrow Connect to Paddington then a cab. Little Venice is actually quite close to Paddington, but getting there on foot or by bus is awkward because of the road layout in the area. You could also get the Bakerloo Line one stop from Paddington to Warwick Avenue, but there are long escalators at both stations that might be awkward with luggage.
Been there, done that coming from CA's West Coast. Make it easy on yourself and cough of the $'s for the Heathrow Connect or Express to Paddington Station. Walk out the front door of Paddington station and queue up for a Black cab. You are in London and one of the best traditional aspects of being there is taking a Black Cab. Drivers must of pass a test to be a Black Cab driver and it takes 3 years to learn ALL the streets of London to pass the test. Nobody knows London better than Black Cab drivers. Nobody. Those cabbies are great resources for inside information and will get you to Little Venice, no muss, no fuss. You can save money elsewhere. Great city. Have fun.