We took the London Underground from Heathrow Airport to our hotel, near Gloucester Road Tube station.

If you arrive in London early in the day, it may be worth it to get a Day Travelcard. We arrived on a Saturday, so we opted for the off-peak (for weekends, or after 9:30am weekdays) One Day Travelcard for unlimited travel. Make sure your ticket covers all zones. Heathrow Airport in located in Zone 6 and central London is mostly in Zones 1-2.
Depending on how you go, there are two ways to exit Heathrow Airport via the Tube:
1 – The Heathrow Express will take you directly to Picadilly Circus Tube stop in about 15 minutes. There is a different (and more expensive) fare for this ride.
2 – Take the local train line (Picadilly line) into Central London. This is the inexpensive way to get into London, and obviously takes longer (about an hour). I used this method to get to our hotel.
Also, it’s best to check the Underground’s weekend service advisories online before arriving. Two of the main Underground lines were suspended the weekend I was there.